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Published: Saturday, 05 October 2019 23:34
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Stores:

Shopping sections lists all the things that you shop in your daily use.

This section provides general references to all the stores from where you can buy things from. However, specific deals won't be posted here, but in the deals section. Credit cards and Bank account deals are in finance section. Shopping is categorized into following:

  • - laptops:
  • - phones:
  • - groceries
  • - gas:
  • - clothes
  • - toys
  • - medicines
  • - miscellaneous

 

Before we get into the stores, let's explore different ways to save money on sales tax as well as any rebates offered by government, utility companies or other private companies.

 

 

Sales Tax holiday:

Most of the states in USA charge sales tax except for 5 states - Alaska, Delaware, Montana, New Hampshire and Oregon. However among states which charge sales tax, there are some that give you sales tax holiday once or twice a year. Different states have different sales tax holiday during different times of the year. You can save about 10% or so depending on the sales tax rate. Below are some sales tax holiday days for various states.

TEXAS:

Texas has sales tax holiday 4 times per year on different items - during April (on emergency products), May (on energy efficient and water efficient products) and August (on clothing, shoes, etc). You can get more info on this website: https://comptroller.texas.gov

Link for various tax holidays in texas: https://comptroller.texas.gov/taxes/sales/faq/tax-holidays.php

Appliances: In Texas, the only time to buy appliances is during memorial day weekend. They have sales tax holiday for buying any energy efficient or water efficient appliances. Energy efficient appliances need to show "ENERGY STAR" logo on them in order to qualify. Water efficient appliances need to display "Water Sense" logo. Most appliances as Refrigerator, washer, dryer (dryper only qualifies if it's part of washer dryer combo unit, and not sold separately), ceiling fans, shower heads, dishwasher, etc qualify. With appliances prices so high, you could easily save $100-$200 in sales tax. On top of that, most retailers as Home depot, Lowes, Costco, BestBuy will have good sales on Memorial day weekend. If you shop around, you can get pretty good discounts on these.

For various years, here's the link (it gets updated with the latest year): https://comptroller.texas.gov/taxes/publications/96-1331.php

2023: May 27-May 29:

2022: May 28-May 30: https://comptroller.texas.gov/taxes/tax-policy-news/2022-april.php

 

Back to School items - clothing, footwear, school supplies: You don't pay sales tax on selected items during the back to school weekend, which is usually in first or 2nd weekend of August. It takes place a week before public schools open for new academic year.

For various years, here's the link (it gets updated with the latest year): https://comptroller.texas.gov/taxes/publications/98-490/

2022: Aug 11 - Aug 13:

2022: Aug 5 - Aug 7:

 

Federal rebate:

2017-2021: There is $500 federal rebate available for buying lots of energy star efficient appliances. It expires at end of 2021. It's limited to $500 per taxpayer over his lifetime. So, if you haven't taken advantage of this $500 credit, buy something that you might need in future by end of 2021. If you bought something in past, and didn't apply for this rebate, you can file amended return for that year and claim the credit.

Here's the link for the $500 rebate: https://www.energystar.gov/about/federal_tax_credits/non_business_energy_property_tax_credits

 

P&G rebate:

This rebate is offered by P&G every year, and is valid no matter from where you bought your P&G products. It's valid on limited number of P&G items, so check the rebate form before you buy items. You need to make an account on this link: https://www.pggoodeveryday.com/rebates/

Once you have an account, you can see current rebates. Their rebates usually run for 3 months, once or twice a year, and you get $15 off $50 or more, so 30% savings on top of whatever discount you get from the store. This is all online, so you don't to spend any money on stamps, and P&G is pretty good at honoring these. I never had any issues getting the reward card from them. See in deals section for any active rebates.

 

 

Merchants:

These are some of the most value oriented merchants or websites listed below. I'll list specific items later. I'm listing the US version of the website, as deals are usually available only on US websites.

walmart.com: Walmart is the behmoth in retail They advertise "low prices", but their prices are low only for people who need to buy something right now. They have close to the lowest price for any item on a given day. However, there are usually coupons, sales, etc at other stores from time to time, where you can buy items for a lot price than walmart's price. People who are willing to wait for dales or deals can find stuff for about half the price of what they can find at walmart. So, I don't recommend shopping at walmart, unless you find items on sale or are cleaning their clearance racks (with > 50% discount) or need something right now due to an emergency. The only good thing about walmart is tat their return policy is very good, and almost everything can be returned in 30 or 90 days.

  • Verdict: Walmart is a very good store to buy anything that you can find on sale. Definitely better than amazon and ebay. Walmart also has lots of items on clearance in their stores, which are really very cheap. I would certainly buy from walmart any day over amazon and ebay.

amazon.com: amazon is the biggest online merchant. It used to have a lot of deals,  but lately it's prices are the same as walmart on most of the stuff. Amazon doesn't allow price adjustment anymore, so if the price of item goes down, you are out of luck. Good news is that it allows many items to be shipped back free of any charge (just look at the return policy mentioned for the item you are buying), Almost all the items have 30 day return window. Buying from walmart is usually better, as you can return the item and rebuy it, incase the price goes down in the next 30 or 90 days. Walmart has a 90 day return window for items sold by walmart, so much better return policy there. Amazon also requires yu to spend $25 in a single order in order to qualify for free shipping (unless you have prime membership, which in itself is pretty expensive at > $100 per year)

  • Verdict: Amazon is lot better than ebay, but is still very uncompetitive when compared to walmart. Walmart has longer return window (90 days vs 30 days for amazon). Walmart allows free shipping for most of the items sold by 3rd party sellers on it's websites (unlike amazon which reuires you to purchase atleast $25 worth of items). Retuens at amzon are easy (just goto store to return it). So, if same item is available at walmart even for a few bucks more, I would advise buying it from walmart.

ebay.com: ebay is a good website to buy cheap chinese items. Many of the US sellers on ebay are present on amazon.com too, so you may want to check the price on both of these websites to see where it's cheaper. A few times every year, ebay offers 5% ebay bucks, which gives you 5% back in ebay credits to use on anything at ebay in the 1st month of next quarter (for any ebay bucks earned in previous quarter). They charge sales tax on every item sold on ebay, and 5% ebay bucks are mostly useless. You do get 1% cashback by using some cashback websites as topcashback.com. Sometimes ebay has special cashback of upto 10%, that may be the only time when ebay might be competitive with amazon.

Until 2018, ebay was a very good website, which regularly offered coupons of 20% or more on any ebay item, sold discounted giftcards, allowed you to buy gold/silver with ebay gift cards, but all those good days are gone. Now ebay is just a ghost site, trying to maximize profit from whatever buyers it has on it's site.

You may want to buy discounted ebay Giftcards to use on ebay. They are rare to find. Sometimes AMEX credit cards give you offers of "$25 in credit for spending $250 at BestBuy". You may buy ebay GC in store with such offers. Once any money on ebay Giftcard is used on ebay, it gets locked to that account, so it can't be hacked. However, ebay giftcards just have a 13 digit redemption code (with no PIN), so it makes it vulnerable to hackers. Although so far, I haven't seen any of my ebay GC getting hacked. This is the link to check your ebay GC balance:

https://www.ebay.com/gft/balance

  • Verdict: ebay is a risky website to buy anything expensive. You should use it to buy cheap chinese stuff (<$10 like phone cases, led, transistors, etc), definitely no electronics over $10 (unless it's from a big retailer or manufacturer as BestBuy, Black and Decker, etc). There is no central support (individual sellers selling items who don't care). After 30 days of placing an order, there's nothing ebay will do to resolve any issue. Many of these items take more than 30 days to be received, so you are out of luck by the time you receive your item. Most of the items have a 30 day return window, but they require you to pay return shipping. That is why some of the sellers on ebay are able to sell low quality items. Just not worth all the hassle. If the same item is available on amazon from the same seller even for a few bucks more, I would advise buying it from amazon. At least amazon will allow you free return (no return shipping), and a better customer support than ebay.

groupon.com: Groupon is a good website to get hotel deals, restaurant deals, beauty deals and attractions (things to do) in different cities. You get cashback of up to 10% most of the times (on cashback sites, usually swagbucks gives 10% cashback). There are also coupons every week for extra 20%-30% off. With all of these, your final price is 50% of the original price (usually cheaper compared to buying thse services elsewhere).  As of 2023, the service has gone downhill, refund is very difficult, and almost all sales are considered final. Even if the merchant doesn't honor Groupon, Groupon won't give a you a refund. In the past, they allowed users to exchange any unused Groupon deals with any deal on website, but NOT any more. So, be aware of what you are getting in. 

  • Verdict: Before you buy any service, check the price on groupon. Most of the merchants on Groupon are well rated, and I never had trouble. Buy only when you are 100% sure to be using that Groupon, and use a credit card. Use that Groupon within 30-60 days so that in case of that Groupon not working, you can dispute it with the credit card company.
  • Avoid buying Groupon GC for 2 reasons: 1. You don't get cashback and 2. Refund is almost impossible (no dispute can be filed as it's not a credit card). I used to buy groupon GC at 10% discount and use it on groupon along with cashback before 2022.  

wayfair.com: For cheap furniture, this is a good website as it has awesome customer service. If you have any parts missing, they will usually refund you very generously, or send you a replacement product for free. However, furniture from here are not too heavy (price per kg of wood is not very lucrative), but they are good looking. Prices are good too. Usually you can find a 10% off wayfair coupon anywhere (usps moving package, flyers, new customers, etc), so that saves extra 10%. Don't be fooled by their "original prices" as they are jacked up at least 3-5 times.

  • Verdict: Check the price of anything you buy from wayfair at walmart and amazon. You may be able to get almost same item at lower price. The only good thing about wayfair is their superb customer service. They refund partially (10%-30% of price) for any damage that you claim without requiring any proof (a lot of scope for abuse here).
  • You can buy wayfair giftcards at grocery stores for 20% when they are on sale. Accumulate those until it's time to buy something.

UPDATED 2025: 2 new stores that have come on my radar are aliexpress and Temu. Both of these offer the same quality of merchandise than amazon, walmart and ebay offer, but for much lower price. Icing on the cake is that CashBack offers from portals is usually around 20%-40%. If you wait for such CB offers, and make a purchase for items shipped by local warehouses in USA, you end up saving 75% off the price that Amazon sells for. Absolutely nuts:

aliexpress.com: Anything that you can buy from ebay, amazon, etc, it's most likely sold here for a much lower price. It's not all shipped from China, but they have local warehouses too. If it's shipped from within USA, it's not subject to tariffs (as of 2025). Also, 20%-30% CB is available at least once a month via CB portals.

temu.com: Similar to Aliexpress.com, and similar prices. Also, usually higher CB is available than aliexpress. Upto 40% CB is available once every month or so. The merchandise listed on temu is more geared towards clothes and fashion, but you can still a lot of other things.

 

 

Pharmacy/Drug Stores: These CVS and Walgreens are the 2 biggest medical stores, where you can get all your medical supplies. They are called Pharmacy stores. Walmart, target and most other grocery stores also have pharmacy section, and you can usually find all your medicines over there too. There's no difference in price for prescription medicines, since those prices are dictated by your insurance companies, and NOT by your pharmacy stores. So, there's really no preference in picking up medicines from CVS/Walgreens.

 One thing to note is that CVS and Walgreens carry a lot of other day to day items as toothpaste, beauty supplies, bread, milk, photo, etc. Most of the stuff is way overpriced, but they usually have coupons to offset their high prices. Even with the coupons, their prices are high. However, from time to time you may be able to find good deals, where you can stack multiple coupons. Walgreens usually has lot more deals than CVS. I haven't found any worthy deal at CVS in 2020 or 2021. However at Walgreens, I've found lots of deals, including free toothpaste, free photo, very cheap nuts, razors, etc. So, stick with walgreens if you are looking to get some free stuff every year.

Walgreens: Walgreens is my favorite store in 2021 for it's awesome deals (mostly items for free after reward points). Any deals at Walgreens are posted in our deals section. The most common deal at Walgreens is free photo (usually 8x0, 5x7 and 4x6 photos). You can find those deals in"photo" section. Other common deal is discounted Gift cards for Kohls, Macys, dominos, etc couple of times every year. You can find these deals in our "gift card section". You can usually pick toothpaste, toothbrush, mouthwash etc for free (after reward points) couple of times a year. Walgreens has great rewards program. You need to sign up in store/online (it's free) and get a "Balance reward member number". Now you can connect this card to your phone number or online walgreens account. You start earning 2 kinds of rewards with the Walgreens Rewards membership:

  • Walgreens cash rewards (WCR): These are more popular rewards. Walgreens usually offer reward points on lot of purchases. These reward points don't expire for  a year since you receive them, so you can use them at your leisure (they expire in 6 months if your account is inactive). You do get 1% WCR on everything that you buy at Walgreens including prescription. So, I buy all my prescription supply from Walgreens (even though their pharmacy department is worse than CVS, it's only couple of times a year that you need to deal with them). They also offer coupons once a month or so for something like $4 rewards on $20+ purchase. You shouldn't use existing WCR for making such purchases which require you to spend a certain amount of dollar, as sometimes those invalidate the coupon and you don't get the reward point. However, reward points can be used on offers like "get $2 WCR on buying one colgate paste", since these don't require you to spend a dollar amount of money. Your total needs to be above $20 before manufacturere's coupon (on coupons like $4 rewards on $20+ purchase), but after applying other coupons (walgreens coupons, etc), and before taxes.
  • Walgreens Register Rewards (WRR): These are less common and are given for in store purchases. They just get printed in store receipt. These expire within 7 days. If a offer says, that you are going to get certain WCR for purchasing something, and you don't see it printed on the receipt, you didn't get it. I don't bother about buying items which have WRR rewards, as it's hard to know if you are going to get it or not. they also expire so quick, that they are mostly worthless.

Keep in mind that even though "estimated" walgreens rewards may show on your order in your email and in your pickup receipt, but they may never appear in your account. The promotional rewards may not apply correctly to your account. So, always check your account for your rewards points after you pick up your order. If they don't show up, chat with customer service. If they apply those reward points, fine, else just return the order. Reward points apply automatically if all conditions have been met. Cancelled orders mess up reward points, so always check your rewards on cancelled orders. Sometimes rewards never show up for some orders. Customer service told me it's because I redeemed points, or my order got partially cancelled or the order just didn't qualify for additional points. Chat with them nicely, and most of the times they will give you "free reward points" as a goodwill gesture.

One other nice thing at Walgreens is that after summer, christmas, etc, they have tons of items on clearance. Most of them are 75% off. sometimes you will find stuff at 90% off, which is as good as it can get. Kids toys, swimming kits, candy, back to school items, decorative stuff, over the counter medicines, etc go for a dollar or two. Best time to buy summer clearance is in September. For Christams clearance, January is the best.

UPDATE 2023: Minimum order of $10 for free store pickup => Walgreens has now implemented this policy of Minimum $10 of order (After coupons, promo codes, etc) for free store pickup. It's hard to find "on sale items for $10", as they will have just 1 or 2 items on sale at a given time. This is nice little trick to get around it as posted on slickdeals:

  • TRICK: You don't have to fill $10 for free pickup. Add an expensive item into the cart to take the total over $10 and proceed to continue to checkout until you are in the review screen. Open the cart in another browser tab. Remove the expensive item. Go back to the original tab and continue checkout. It will let you checkout with pickup with the expensive item removed. I've tried and it works every time.

CVS: I would avoid CVS as of 2021. CVS has really dried up on deals. Free Toothpaste are once a year deal at CVS. They also have free 5X7 photo offers couple of times a year, but not as often as Walgreens. They have also their "Extra bucks (EB)" reward program, similar to Walgreens. You just need to sign up for CVS membership (it's free to join).  Most EB expire within 7 days, and it's hard to find something to spend it on, since everything is so overpriced. It's unlike walgreens where you can wait to buy stuff as WCR don't expire for a year. Not with CVS. CVS as a store is dead, as I could never find anything to buy here anymore (this is for year 2021). I had a free $1 EB. I searched the store for 30 minutes, and still couldn't find anything to buy at all. Everything is overpriced by at least 2X. I finally threw away the EB. That's how bad it has gotten :(

With both Walgreens and CVS, my strategy is to always buy items that are cheap after instant discount. You combine your available offers with other rewards and coupons and get things really cheap, especially the items that are on sale/clearance already. Items which give you points on purchasing something are a hit or miss, so it's for those who understand the risk.

FLU SHOTS/ COVID VACCINES: All major Pharmacy chains offer some coupon for getting a FREE Flu shot. The flu/covid shots/vaccines are themselves totally free (covered by almost all insurance). Walgreens has been a leader in the game, offering $10 off $10+ coupon  or $20 off $20+ coupon in the past for getting fluu/covid shots. I've used it to buy a lot of lot of stuff on clearance with these coupons. Other stores offer $5 off coupons only.

Link for Flu shot deals:

 

Dollar Stores: There are about 35K dollar stores in USA that sell items for a dollar. some of these dollar stores also sell items for $2, $3 etc, but most of them have everything for a dollar. These stores are very expensive, and only good for buying emergency things that you need right now, as phone cable, helium balloons, party supplies, etc. Printed helium balloons are always $1 at Dollar general, and those are the cheapest helium balloons you can find anywhere. Everything else is expensive, so run away after you have bought those balloons.

Dollar General (DG) is the largest dollar store chain, followed by Dollar Tree (DT) and Family Dollar (FD). These 3 dominate dollar store retail footprint. Sometimes, these stores have discounted Gift Cards, which may be worth buying (only if they are at 20% or more off)

Here's an article showing how much profit dollar stores make: https://thehustle.co/the-economics-of-dollar-stores

Kohls / Macys / J.C, Penney: These 3 are one of the best places to buy your everyday items as clothes, kitchen utensils, decorations, small appliances, bedroomsheets/blankets, towels and tons of stuff like this. JCPenney is bankrupt now (as of 2021), but the stores and the website is still there. They still have offers, but being a bankrupt company, don't expect good offers. Kohls is cheaper than Macy's.Both stores have highly inflated prices, so don't be excited if you stuff selling at discounts of 50% or more. The discount has to be 80% or more for it be a fair price.

  • Kohls gives you Kohls cash from 20% to 40% depending on the sale, which has to be used within 10 days or so (the stores will give you a bonus period of a week or so if you have the physical KC with you).
  • Kohls usually has 15% to 30% off coupons. they also occasionally send 40% off mystery coupon (valid for a day). This can bring the price way down.
  • Kohls is worse than Macys in terms of free shipping. In the past, if you almost always find a code for free shipping on Kohls, but not anymore. You have to meet minimum spend of $75 to get free shipping. A lot of their items even though available in store, won't be eligible for store pickup, so you will have to pay for shipping.
  • Macy's always has free shipping on $25+, and also allows almost all items to be picked up in store for free. This is lot more consumer friendly than Kohls
  • Both Macy's and Kohls GC can be found at 20% off at grocery and drug stores at least once a year.
  • Kohls has a limit of 4 GC per order, while Macy's has a limit of 5 GC per order. Kohls website has no way for you to manually choose which GC to apply. You have to add GC to the wallet, and then there's no way to delete it. then system applies top 4 non zero GC from the wallet. This can really screw you up in using GC on Kohls website. No one from chat or phone can help, because it's hardcoded into the sytem as of 2021 (this is just one more way Kohls screws up it's customers). Using GC at Macy's is lot easier, since GC are never tied to the account.
  • Slickdeals regularly has $10 in rewards on $25+ purchase. I buy from Macy's only during these promotions, as it saves nice $10.
  • Macy's is higher tier shop than Kohls, so you can expect to find better quality/fashion stuff at Macy's than at Kohls.

 

Home Depot / Lowes: These are the 2 biggest home stores, where you can find all your home related supplies as appliances, garden, fans, lights, tiles, carpet, wood, etc. Lowes used to be the better of the two until 2020. Lowes used to have 20% coupons that you could find almost anywhere, as well as a lot of stuff on clearance. However, thinhs have changed at Lowes with their new CEO, No more coupons, sales, clearance, etc. The only thing discounted at Lowes is their Gift cards, which you can get at 10% off almost everywhere. Home depot is a better option now, as it has lot more sales, and gives movers coupons or other coupons for 15% off. Lowes and Home Depot match each other's prices, though not always. I recommend sticking with home depot, as you can find stuff cheaper at home depot. I've had around $500 worth of Lowes GC, that I haven't been able to burn for the past 24 months (as of 2022), because whatever I plan to buy is available for cheaper for Home depot, and Lowes refused to match Home depot's prices (due to multiple reasons as item not having the exact upc code item below their cost price, etc). Home Depot is no saint either :) Things keep changing, so keep yourself informed. For now, there are still coupons available on ebay and few other sites, where you can buy coupons. These are legitimate (few that I tried so far). I've listed the sites below:

  • coupon500: https://coupon500.com/ => I've tried their online coupons few times. They are sent immediately and they work. You have to pay about 10% of coupon price though (not free). UPDATE: As of 2023, all coupons on this site only apply on NON-SALE items. So, basically the coupons are useless.
  • ebay: www.ebay.com => Search for "Home Deopt coupn" or "Lowes coupon". You usually get 10% or $10off or $20off coupons for $5 or so. Read the fine print on coupon though. UPDATE: As of 2023, most of the coupons only work on NON-SALE items. Buy witha credit card that can protect you in case things go south.

 

Harbor Freight (HF): This is an alternative store to Home Depot/Lowes, and is a lot cheaper than both of these big stores. The quality is good, and you can buy extended warranty if you want peace of mind. However, they may not be present in all big cities. Their stores carry tools, garden supplies, plumbing parts, etc. They don't carry furniture, appliances that homeDepot/Lowes carry. One good thing about HF is that they have coupons for couple of free items almost every week. These include flash lights, screw drivers, towels, etc. Look in "Homeowner items" section.

 

 

BestBuy: BestBuy is the biggest electronics retail store, and is able to offer good prices during big sales event. However, their offers have almost dried up as of 2020. Deeply discounted items are always out of stock. The only reason to buy from BestBuy is if you have their GC bought at a discount of 20% or more, which you need to unload. Also, since they are brick and mortar stores, you can always return an item even if bought online. I'm usually able to find better prices at Walmart, ebay and amazon, so I don't shop at Bestbuy at all.

 

Dell.com: This is the one of the companies that is considered boring, but I've bought some best value laptops from here. They usually have 10%-15% cashback on cashback websites as ebates.com, topcashback.com, and also on slickdeals.net rewards program. You can get 10% off coupon for signing up on their website: https://www.dell.com/preferences/signup/. Use any junk email to signup, and wait for 10% coupon to come in email. Usually takes couple of hours to how up. You can still use your original account to use this coupon. On top of these, American Express credit cards have promo for "20% off or $120 off $599" a lot of times. Chase/Bank of America cards laso have 5% in rewards for purchasing from Dell.com. This all can give you extra discount of 30%-40% on top of the sale price. I've bought Dell G15 Ryzen gaming laptops for < $500 after accounting for all the discounts. I've been using it for 2 years with no issues. It's hard to find quality gaming laptops at this price.

 

 

Warehouses: 2 big warehouses are Sam's club (owned by Walmart Inc) and Costco. They both charge yearly membership fees of about $50/year (costco is $60/year). But you can always find deals where you get the membership for free. Both stores sell things in bulk, so you have to buy multiple pieces of same thing. They both advertise saving you money over general merchandise stores. Costco is the one which more people join, as it has better prices, and a lot more generous return policies. However, both of these stores have limited hours, are usually far out, and the amount of money you save is eventually $0, when you price in your gas cost, time cost and the absence of super discounts. A lot of people claim that the quality of items is superior. After 1 year of membership at costco, I haven't found any great prices. I can't comment on the quality, since quality for me is just phenomenal at all the stores (compared to third world countries).

samsclub.com: SamsClub is similar to walmart for most purpose, except that prices are a little lower and quality little better. Best deals from samsclub are gift cards which are usually discounted from 10%-30% off (usually food place GC). Walmart GC may be used at samsclub too. Gas prices are usually cheaper.

costco.com: Costco has much better deals than sams club, and gas prices are lower too. Customer Service is great. Auto services and many other services have much better prices, and free extended warranty. Costco in store only accepts Visa cards, but costco online allowed all 3 - Visa, MasterCard and Discover to be used (No Amex allowed). However from Nov 15, 2023, Discover card would no longer be accepted on their online portal. That is a bummer, as Discover did have their rotating category as "Warehouse purchase" where you got 5% cashback. That is gone for good now. Here's the link => https://www.doctorofcredit.com/costco-com-stops-accepting-discover-card/

NOTE: costco has automatic price adjustment for anything bought online within last 30 days. For in store purchase, you will have to call or go to the store. Link => https://customerservice.costco.com/app/answers/answer_view/a_id/628/~/price-adjustment---costco.com-orders

Membership Fees: However, it doesn't hurt to get the membership to any of these, when it's free or better. Sam's Club Membership go for free couple of times a year (cashback portals, credit cards offers as well as groupon deals). Costco goes for free at most once a year thru groupon or some other deal website. Below are few of their membership deals:

PRO TIP: I got this from DoC => Costco Memberships usually run until the end of the month. If you start it in July 31st 2024, your membership is going to expire July 31st 2025. But If you start it on August 1st 2024, your membership will expire August 31st 2025. So, you get extra 1 month by starting it towards start of the month.

 

 

 

DEALS:

 

 

2024:

 

 

 

09/15/2024: P&G - $15 rebate on $50+ for P&G selected items bought from any store: valid 09/15/24 to 12/29/24

Here's the link: https://www.pggoodeveryday.com/rebates/

There are 3 active rebates going on:

  1. Holiday Savings rebate from 09/29/24 to 12/29/24 => Only 1 per household. Buy $50, get $15 rebate.
  2. Score Big rebate from 09/15/24 to 12/29/24 => Only 1 per household. Buy $50, get $15 rebate.
  3. Olay rebate from 09/01/24 to 12/31/24 => Only 1 per household. Buy $30, get $10 rebate.
  4. Good as Gold Rebate from 04/17/24 to 09/08/24 => 2 per household. Expired

Slickdeals thread: https://slickdeals.net/f/17757786-p-g-score-big-rebate-spend-50-get-15-or-5-20-9-15-24-12-29-24

Same offer as last time. Limit is only 1 per household fr each rebate type. Last offer just expired.

UPDATE Oct 6, 2024: Target has $15 GC on $50 purchase from 10/06/24 to 10/12/24. You can buy $50 worth of Tide liquid detergent or Cascade dishwasher gel. This will only count as $35 of spend (as receipt shows $15 subtracted from Total for Target GC). You can either spend $15 more at Target or buy from Walgreens or local grocery store which have sale/coupon on purchase all the time. Target's price for Cascade is really low with the GC, so stock up on it via this weekly sale.

Link => https://slickdeals.net/f/17795772-target-circle-week-offers-15-target-gc-w-50-select-household-essentials-purchase-many-more

 

 

 

 

2023:

 

 

 

11/14/2023: Ebay 5% off (max $50 discount) with code: TAKE5BOFA => expires 12/31/2023

Link => https://www.doctorofcredit.com/targeted-bank-of-america-get-5-off-ebay-up-to-50-can-be-used-10x-with-code-take5bofa/

You don't need a BoA (Bank of America) card. Just use the link below and enter the code at checkout.

https://www.ebay.com/ulk/webview?mkcid=1&mkrid=711-53200-19255-0&siteid=0&campid=5339006474&customid=&toolid=10001&mkevt=1&url=https%3A%2F%2Fpages.ebay.com%2Fcoupon%2F2023%2Ftake5bofa%2F

UPDATE: Some comments suggest you need to click on the link within BoA website, where you see 5% off offer for ebay. Not Sure??

If it works, use it on something expensive to maximize the value. Any discount on ebay is rare now.

 

 

08/01/2023: Costco: 1 year membership for $60 (includes $45 Costco eGC + $40 off $250+ online purchase) => expiry unknown

This deal is slightly better than what was offered in 2022 ($45 GC now vs $40 GC offered in 2022). $40 promo code expires Oct 31, 2023. Available via Groupon. Always pick up groupon GC whenever they go on 15% to 20% sale. That way you use those Groupon GC to buy deals like these (these deals are pretty safe o use your Groupon GC on). 

Link => https://slickdeals.net/f/16828805-new-costco-members-only-costco-gold-star-membership-45-shop-card-40-off-250-coupon-60?src=frontpage

 

 

04/02/2023: P&G - $15 rebate on $50+ for P&G selected items bought from any store: valid 04/02/23 to 06/30/23

Here's the link: https://www.pggoodeveryday.com/rebates/

Slickdeals thread: https://slickdeals.net/f/16557517-p-g-made-to-save-rebate-15-prepaid-mastercard-back-on-50-of-pampers-bounty-charmin-tide-etc-now-to-june-30-2023-limit-2-per-household?src=frontpage

SAme offer as last time. Limit is 2 per household. Many of these are at decent price at walgreens and selected Grocery stores. Also, there are separate coupons for Tide which will stack. You may get $100 worth of Tide products for $30-$40.

 

 

01/01/2023: P&G - $15 rebate on $50+ for P&G selected items bought from any store: valid 01/01/23 to 04/01/23

Here's the link: https://www.pggoodeveryday.com/rebates/

Limit is 2 per household. Many of these are at decent price at walgreens and selected Grocery stores. Also, there are separate coupons for Tide which will stack. You may get $100 worth of Tide products for $30-$40.

 

 

 

2022:

 

 

 

06/20/2022: P&G - $15 rebate for P&G selected items bought from any store: valid 3/27/22 to 6/30/22

Here's the link: https://slickdeals.net/f/15776128-p-g-rebate-spend-50-get-15-or-spend-20-get-5-valid-3-27-22-to-6-30-22

Tide, old spice and head & shoulders are at decent price at walgreens for week of 06/26-07/02

 

 

05/22/2022: Costco: 1 year membership for $60 (includes $40 Costco eGC + $40 off $250+ online purchase) => expires July 11, 2022

This deal is same as what was offered in 2020. Your membership effectively costs $20 only and you get a $40 coupon too for online purchase, when you spend $250+ ($40 coupon expires Aug 14, 2022). It's not hard to spend $250 online. You may buy dry fruits, electronics, clothes, etc. You may also go thru a cashback portal as topcashback, and they give you 10% back on groupon. Or go thru swagbucks to get 12% cashback.

https://www.doctorofcredit.com/groupon-one-year-costco-membership-40-costco-shop-card-40-off-online-for-60/

 

 

Details
Published: Saturday, 05 October 2019 22:09
Hits: 2441

Photo:

In USA, you can almost always print photos for free or very low cost (lower than what it would cost in ink if you were to print yourself).

Free Photo:

You can search on slickdeals.net for "free photo" and you should see any available and past offers. I'll try to put these under deals and also below under "free photo deals". These are some of the popular stores for getting free photo:

1. Walgreens: Almost every other week, they have free 8x10 photo, free 5x7 photo, free 4x6 photo, or 1 cent 4x6 photo. It's usually limited to one use of coupon per account. So, if you are 2 members in household, make 2 accounts on walgreens with 2 email addresses, and that way you can avail 2 free offers every time. These photo offers usually expire in a day or two, so be sure to act fast !!

2. CVS: Just like walgreens, CVS also has free photo offers. However the offers at CVS are fewer, may be once every couple of months. Since 2020, I have seen them, maybe 3-4 times a year.

3. Walmart: Walmart has 4x6 photos available for printing for 10 cents or less. This is an emergency option if you can't afford to wait for free photo. CVS, Walgreens, etc have much higher regular prices.

4. snapfish: This website snapfish.com has free photo offer, along with free shipping a couple of times every year. You also get few free photos for signing up. Search on slickdeals.net.

5. T-mobile: If you download "Tmobile Tuesday" app, you will get multiple freebies every Tuesday. From time to time, you get "10 free photo prints" at CVS. Anyone who is a T-mobile customer (all phone numbers on a family plan) can download the app and take advantage of the freebies.

 

Big Size Photo or Canvas:

If you want big size photo with frames to hang on walls, then you will need to spend money. I'm talking about 18x24 or 20x30 photos or 36x48 photos. These are not printed on paper, but rather on canvas (a  cloth). It looks really nice when hung on a wall, especially if it already comes "stretched on a frame" (frame is not that thick, but good enough). One thing to note is that the image needs to have enough pixels on it, so that it looks smooth when enlarged to these large sizes. Any image with more than 2000x2000 pixels (or more than 4M pixels) will do great. You can click on "properties" for any image on your computer, and that will show you the size and the pixels it has. Any image with size > 2MB usually has enough pixels to get enlarged.

Best website that I've found for printing economical canvas prints is canvasonsale: https://www.canvasonsale.com

You will get much lower prices if you look up their offers on groupon.com. Groupon has 20%-30% off deals almost every month. If you wait for such a deal, and then buy canvas from this merchant, and use a cashback website for purchasing from groupon (topcashback or ebates) , you can essentially get 40% off already reduced price. You can also get groupon gift cards for 10% off, so use those instead of using your credit card.

I had bought 36x48 and 24x36 canvas from above website. They came with "frame" and were carefully shipped. The print quality was amazing. I paid about $25 for 24x36 size and $40 for 36x48 size with shipping included. This is before cashback and before gift card discount. These are priced at around $300-$500 each on their website (which is non sense price anyway). I don't think you can go wrong with this merchant at these prices for these large canvas with frame.

 

Passport Photo:

In USA, passport pictures are pictures needed for use in your passport or other government applications. The photo size requirements for US passport are different than those in India. Here you need 2 inch X 2 inch passport photo. You can get these passport pictures taken in India also, as they know the requirements there too.

To get your passport picture, you either need to goto walmart, CVS, Walgreens or some other stores, which charge you $10 for a pic. You can put your camera to use, and save some money. If you take the photo yourself, it will cost you 10 cents or less, and in the process you will gain a valuable marketing skill on taking passport pictures !!

Website for Passport Photo:

This website creates correct passport size photo on  regular 4x6 photo size.

https://www.idphoto4you.com/

steps:

  1. goto website above using internet explorer. This doesn't work in firefox, as it just doesn't show any option on 2nd screen. If it doesn't work on your browser, try another browser. i can confirm it working on Internet Explorer.
  2. choose passport "2x2" for USA passports, since they require pic of 2 inch by 2 inch. Follow instructions to upload a photo.
  3. Then on next screen, adjust brightness and contrast. Usually not required.
  4. Then on next screen, crop photo. It shows 2 green bars. Your face should be in between those 2 green bars.
  5. After crop, your picture will be ready for download in 1 minute. After a minute, download the photo to your computer. It will have 4 pics of 2x2 on a single 4x6 paper size.
  6. You can print it at any store the same way as you print regular 4x6 pics. You can cut the resulting 4x6 to get 4 passport pics of 2x2 size. It shouldn't cost you more than 20cents as most stores print it for 10 cents or less. I do not print it at my home printer, as it's hard to get good paper. Store printing is cheaper than printing it at home, as printer ink are expensive.

Important tips:

  • Take picture with your camera against a white background. Take picture during day (in shade and outdoors, where light is coming equally from all sides).  Else you may end up getting a shade of your face in the background, which may be a reason for rejection
  • For white background, buy Kid's white paper that they sell under "school supplies" in Grocery stores, Office stores, Walmart, etc. These white papers are about 2 ft X 3 ft, and are thick enough to be placed behind the subject. Just have someone hold the white paper behind the subject, while you take the picture. Don't use clothes as white background, as they develop wrinkles, which reflect light at different angles, causing some weird colors to pop up in printed pictures. These colors may be removed by adjusting contrast/brightness, but not worth it. If you have a thick cotton sheep, that may work out OK.
  • Once you upload picture to any website as CVS, Walgreens, etc, adjust the brightness over there in their software. Do not adjust it in "idphoto4u". I've seen that adjusting brightness in walgreens website, gets rid of any blue or similar color that comes when you take photos with white background. On walgreens website, this is what you do: Under "enhance" option, increase "brightness" and "contrast" to 50% or more (i.e 1/2 of maximum value). You will see that the background getting more and more white. If you get too much contrast or brightness, then the printed photo will get washed out or appear not natural. so, be careful overdoing it.
  • All my photos got rejected for all applications the very first time, because they all had whitish/bluish background, even though I had used "White Paper" as background. I tried adjusting it multiple ways, but nothing worked. The ultimate thing that worked was using walgreens website to adjust brightness/contrast. Don't use any photo editing software to change the background, as those can easily be identified and will be rejected immediately.
  • See the passport website "travel.gov" for various samples of photos. Don't let your application get rejected due to a bad picture. It's just more hassle.

 

Good Luck and happy photography !!

 

 

Walgreens/CVS Free photo Deal => See on link below for updated codes.

This link on doctorofcredit.com lists all codes for 8x10 free photo:

For other codes or other sizes as 4x6, 5x7, etc, search on slickdeals.net or on doctorofcredit.com here =>

Deals:

 

 

 

2023:

 

 

 

01/09/2023: Walgreens 5X7 magnet photo for $1 - Code 5x7MAG (expires 01/10/2023)

https://slickdeals.net/f/16368871-walgreens-5x7-photo-magnet-0-99

 

 

2022:

 

 

12/24/2022: Walgreens 8x10 Free photo - Code SNOWDEAL (expiry unknown)

https://slickdeals.net/f/16336318-walgreens-free-8x10-photo-code-snowdeal-0-00

 

 

12/08/2022: Walgreens 8x10 Free photo - Code ICESK8 (expiry unknown)

 https://www.doctorofcredit.com/walgreens-free-8x10-photo-print-with-promo-code-eightdec/

 

 

12/02/2022: Walgreens 8x10 Free photo - Code FREE-8BY10 (expiry unknown)

 https://www.doctorofcredit.com/walgreens-free-8x10-photo-print-with-promo-code-eightdec/

 

 

10/17/2022: Walgreens 2 of 5X7 Free photo - Code  PAIR

https://www.doctorofcredit.com/walgreens-2-free-57-photo-prints-with-promo-code-your5x7/

Free as always. It's smaller sized 5X7 this time.

 

 

09/19/2022: Walgreens 5X7 Free magnet photo - Code FREE-MAG (expiry unknown)

https://slickdeals.net/f/16046371-free-5-x-7-magnet-at-walgreens-w-code-free-mag?src=frontpage

 

 

08/22/2022: Walgreens 8x10 Free photo - Code EMAILONLY (expiry unknown)

 https://slickdeals.net/f/15991876-walgreens-photo-8-x-10-photo-print-free-free-pickup

 

 

08/14/2022: Walgreens 8x10 Free photo - Code FREE8BY10 (expiry unknown)

https://slickdeals.net/f/15976981-walgreens-photo-8-x-10-photo-print-free-free-pickup

 

 

06/15/2022: Walgreens 8x10 Free photo - Code FUNINTHESUN (expiry unknown)

https://www.doctorofcredit.com/walgreens-free-8x10-photo-print-with-promo-code-eightdec/

 

 

05/02/2022: Walgreens 8x10 Free photo - Code MAYFREEBIE (expires 05/05/2022)

https://www.doctorofcredit.com/walgreens-free-8x10-photo-print-with-promo-code-eightdec/

 

 

04/04/2022: Walgreens 8x10 Free photo - Code RABBITPRINT

https://www.doctorofcredit.com/walgreens-free-8x10-photo-print-with-promo-code-eightdec/

 

 

03/20/2022: Walgreens 8x10 Free photo - Code SPRBREAK

https://slickdeals.net/f/15680635-walgreens-8-x-10-photo-print-free-free-store-pickup

 

 

 

2021:

 

 

12/31/2021: Walgreens 8x10 Free photo - Code ZERO

https://slickdeals.net/f/15539821-walgreens-photo-8-x-10-photo-print-free-free-store-pickup

Last Free Photo of 2021.

 

 

12/25/2021: Walgreens 8x10 Free photo - Code FROSTY8X10

https://slickdeals.net/f/15527032-walgreens-8-x-10-photo-print-free-free-store-pickup

Free as always

 

 

12/12/2021: Walgreens 5 Free 4x6 photo - Code 5FREEPRINT

https://slickdeals.net/f/15496597-walgreens-photo-5-count-4x6-glossy-photo-prints-free-free-store-pickup?src=frontpage

Free as always

 

 

12/03/2021: Walgreens 8x10 Free photo - Code MERRY8X10 => expires in couple of days

https://www.doctorofcredit.com/walgreens-free-8x10-photo-print-with-promo-code-eightdec/

Free as always

 

 

11/14/2021: Walgreens 8x10 Free photo - Code GRATEFUL8X10 => expires in couple of days

https://www.doctorofcredit.com/walgreens-free-8x10-photo-print-with-promo-code-eightdec/

Free as always

 

 

11/12/2021: Walgreens 5X7 Free photo - Code  IGOTMYSHOT => expires in couple of days

https://slickdeals.net/f/15393793-walgreens-photo-5-x-7-photo-print-free-free-store-pickup?src=frontpage

Free as always. It's smaller sized 5X7 this time.

 

 

11/05/2021: Walgreens 8x10 Free photo - Code FALLSMILES => expires in couple of days

https://slickdeals.net/f/15377812-walgreens-8-x-10-photo-print-free-free-store-pickup?src=frontpage

Free as always

 

 

10/30/2021: Walgreens 8x10 Free photo - Code ONEBIG8X10 => expires in couple of days

https://slickdeals.net/f/15364711-walgreens-photo-8-x-10-photo-print-free-free-store-pickup?src=frontpage

Free as always

 

 

09/21/2021: Walgreens 8x10 Free photo - Code 8X10AUTUMN => expires in couple of days.

https://slickdeals.net/f/15293506-walgreens-photo-8-x-10-photo-print-free-free-store-pickup

Free as always

 

 

08/18/2021: Walgreens 6 customized set of 5x7 Free photo - Code FREEHELLO => will expire soon.

https://slickdeals.net/f/15223435-live-walgreens-photo-set-of-6-customized-5-x7-premium-photo-cards-free-store-pickup?src=frontpage

6 customized 5x7 photo set for free. Site was having issues making a photo set, but appears resolved now.

 

 

08/15/2021: Walgreens 8x10 Free photo - Code BIGGER8X10 => expires in couple of days.

https://www.doctorofcredit.com/walgreens-free-8x10-photo-print-with-promo-code-eightdec/

Free 8X10 photo as always.

 

 

EXPIRED: 07/25/2021: Walgreens 8x10 Free photo - Code JULY8X10 => expired on 07/27/2021.

https://slickdeals.net/f/15182485-walgreens-photo-8-x-10-photo-print-free-free-store-pickup

Free 8X10 photo as always.

 

 

Details
Published: Tuesday, 24 September 2019 18:08
Hits: 3200

Matlab is proprietary tool, and it's license fees are in thousands of dollars. Many open source alternatives exist, which are as good or better than Matlab.

1. Octave: GNU Octave is most popular alternative, and has been in development for more than 30 years. It strives for exact compatibility, so many of your projects developed for MATLAB may run in Octave with no modification necessary. So, if already learned Matlab, you can seamlessly start using Octave. It's front end interface can be chosen to be same as Matlab.

2. Scilab: Best known alternative outside of Octave. It doesn't strive for exact compatibility with Matlab, but is very similar to Matlab

3. Mathematica: It offers features for machine learning, image processing, data mining, etc. It is a superior tool for symbolic mathematics.

4. Python: Python language itself supports a lot of packages which can do all the scientific computing done in Matlab. NumPy is the main package for scientific computing with Python. SymPy is another Python library for symbolic mathematics. It's preferred to use python, as you have to learn python or any other scripting language anyway.

 

 

 

Details
Published: Monday, 23 September 2019 18:03
Hits: 3265

Examples of few common signals in Fourier domain:

When we transform signals from time domain to frequency domain, it's just like any other transformation in maths. A function takes inputs, and transforms it. If there is 1:1 transformation, then we can recover the original input, by applying inverse function to output. However, one thing that stands out in conversion from time domain to frequency domain is that frequency domain bears resemblance to physics. It's easier to visualize sound waves in terms of frequency, so most of the examples about fourier conversion talk about sound waves, but fourier conversion can be applied to any data.

This link shows proof of FT of some common functions: http://www.thefouriertransform.com/pairs/fourier.php

Let's intuitively try some conversion from time domain to freq domain for the below waveforms for all 4 fourier domains: CTFS, CTFT, DTFS, DTFT. Then we'll do rigorous calculation to verify it:

1. Constant signal: This is a signal which is a constant value for all times (-∞ < t < ∞). Since this signal has no variation at all, we don't expect to have any sine/cosine waveforms to reconstruct this dc signal. Infact just the DC offset would be enough to construct this signal. So, in frequency spectrum, we don't expect to see any freq component except f=0 (DC signal).

CTFS: We assume signal to be periodic with arbitrary period T0. We can do this since an infinite long constant signal can be broken into finite duration signals.

Ck = 1/T0 ∫ x(t) e-jω0kt dt = 1/T0 ∫ 1 * e-jω0kt dt = 1/T0  [e-jω0kt ] /(-jω0k) with limits = +T0/2 to -T0/2. For all non zero values of k, Ck = 0. For k=0, we do not integrate (since integration not possible with k in denominator), instead we do C0 = 1/T0 ∫ 1 * dt = 1.

So, only at f=0, we get C0 = 1, all other freq components are 0 as expected.

CTFT: Since for CTFT, signal can be aperiodic, we can compute CTFT of dc signal directly

X(ω) = ∫ x(t) e-jωt dt = ∫ 1 * e-jωt dt = [e-jωt ] /(-jω) with limits of t = +∞ to -∞. However, this doesn't converge to any value, as e-jωt = cos(ωt) - j.sin(ωt) = which oscillates as t->∞. So, we guess that the answer is delta function. If that is true, then x(t) = 1/(2Π) ∫ X(ω) ejωt dω = 1/(2Π) ∫ δ(ω) ejωt dω = 1/(2Π). That implies that X(ω) = (2Π) δ(ω).

Here again, we see that for constant function, freq component exists only at ω=0, with magnitude=2Π

DTFS: If we take discrete samples of constant signal, then we get a signal which is 1 at all samples. Again, treating the signal as periodic with period T0, with N samples in that period, we can compute DTFS.

x[n]=1 for n=0 to N-1. 

Ck = 1/N  ∑ x[n] e-j(2Π/N)kn = 1/N  ∑ 1 * e-j(2Π/N)kn for n=0 to N-1.

Now, we can calc exponential sum formula ∑ ejkn for n=0 to n=N-1. This is same as sum of geometric series = (1 - ejkN) / (1 - ejk) = sin(1/2*N*k)/sin(1/2*k) * ejk(N-1)/2

So, Ck = 1/N  ∑ 1 * e-j(2Π/N)kn = 1/N  * (1 - e-j(2Π/N)kN) / (1 - e-j(2Π/N)k) = 1/N  * (1 - e-j(2Π)k) / (1 - e-j(2Π/N)k)

For k=0, Ck = C0 = 1/N * ∑ 1 * 1 = 1/N * N  =1

For k≠0, Ck = 1/N  * (1 - e-j(2Π)k) / (1 - e-j(2Π/N)k) = 1/N * (1 - 1) / (1 - e-j(2Π/N)k) = 0

Here, just as in CTFS, only at f=0, we get C0 = 1, all other freq components are 0 as expected.

DTFT:  Here, again we have discrete samples, but signal is considered aperiodic. So, we can compute DTFT directly.

x[n]=1 for n=-∞ < n < ∞.

X(ejω) = ∑ x[n] e-jωn = ∑ 1* e-jωn = with limits of t = +∞ to -∞. However, this doesn't converge to any value, for same reasons as CTFT. So, we guess answer as δ(ejω)

=> x[n] = 1/(2Π) ∫ X(ejω) ejωn dω = 1/(2Π) ∫ δ(ω) ejωn dω = 1/(2Π). That implies that X(ejω) = (2Π) δ(ejω).

So, as expected, freq component exists only at ω=0, with magnitude=2Π

DFT: DFT is same as DTFS. We can compute DFT by taking N samples of DTFT

DFT Xk or X[k] = samples of X(Ω) at discrete freq =  X(Ω) | ω=2Πk/N where 0 <= k <= N-1.

Since X(ejω) = (2Π) δ(ejω) => X0 = (2Π), X1 to XN-1 = 0 as delta function is 0 everywhere else. Result is same as DTFS, except for factor of (2Π) .

2. Impulse signal: It's denoted by δ(t). This is a signal which has a finite value at t=0, but is 0 everywhere else. For analog signals, it's impossible to construct such a signal (since analog signals need to go from 0->1 and then back from 1->0, which will always take a finite amount of time), but mathematically in the limit t->0, we can approximate such a signal. For discrete signal, such a signal is possible to construct by having sample at t=0 as "1", and "0" everywhere else. It's hard to visualize what freq components such a signal would have. But, we do observe that impulse func is an infinitely steep signal in limiting case where t->0. So, it should have infinite freq component in it. It should also have a DC freq component in it, as it's avg value is "1", and not "0". It turns out that such an impulse signal has all freq components from 0 to ∞, of equal magnitude. We can derive this by employing duality property of FT, where taking fourier of frq domain func, gives time domain function back. So, if we have constant signal in time domain, we get impulse func in freq domain, as we saw above. So, constant signal in freq domain will give impulse signal in time domain. That is how we get constant function in freq domain by using duality theorem.

3. train of impulses: It can be rep as periodic impulse func.

4. Sine/Cosine wave: This is a sine/cosine wave with a given freq. It may have a net dc value depending on whether the waveform is shifted up/down from y=0. If it has a net dc value, the only difference in freq spectrun would be that it would have a dc component (f=0) in it's freq spectrum.

A. periodic:

CTFS: It will have only 1 freq component at the freq of sine wave itself. So, Ck will be non zero only at that freq (all others will be 0). This can be seen intuitively as FS is summation of sine/cosine, and this waveform is exactly same as one of the terms, so no other terms of sine/cosine needed to make up this waveform. It also has dc freq component (at f=0) if the square signal has net +ve avg value.

CTFT: We can compute CTFT for any func, periodic or aperiodic. So, we compute CTFT for this signal, and expect to get same result as CTFS. However, as we explained in signal processing page, CTFT is an integral, and hence continuous. So, we'll get impulse function at each of the freq component instead of getting a single discrete line, as we get in CTFS.

B. non periodic: DTFT computed. It will be cont freq spectrum, with freq component similar to DTFS. However, now it's an impulse function centered at ω=+ωk and ω=-ωk.

For x(t)=sin(ω0t) => X(ω) = (2Π)/i * 1/2 * [δ(ω-ω0) - δ(ω+ω0)] => 2 soln are +Π/i and -Π/i at ω=ω0 and ω=-ω0

For x(t)=cos(ω0t) => X(ω) = (2Π) * 1/2 * [δ(ω-ω0) + δ(ω+ω0)] => 2 soln are +Π and +Π at ω=ω0 and ω=-ω0

3. Step signal: This is a step signal, going from 0 to 1 at certain time t.

4. square signal: This signal can have any duty cycle. It's 1 for a while, and 0 elsewhere. It can be thought of as a +ve step signal followed by -ve step signal.

A. periodic: For periodic sqaure wave, we have CTFS, which has freq component at freq=1/T, 3/T, 5/T (i.e odd harmonics). It also has dc freq component (at f=0), if the square signal has net +ve avg value. F

B. non-periodic: For non-periodic square wave, we calc CTFT, which turns out to be a sinc func, where sinc func is defined as sinc(t) = sin(Πt)/(Πt)

5. rectangular signal:

6.

 

Matlab: We can use Matlab software to plot these functions. We use fourier function to calc FT for any function. There is no func for giving FS of periodic func. Instead, we have to solve the series for FS, and have the result plotted. FT is easier to calc using in built "fourier" func, and it can be done for both periodic and aperiodic signals.

Matlab code for plotting the CTFT is:

syms x;
f = exp(-2*x^2); %this is the func whose FT we want. We'll replace this func with our desired func below.
FT = fourier(f); %calculates FT(w) for given f(x). FT is calculated in terms of radians (w)
ezplot(FT,[-1000,+1000]); %plots FT(w) over -1000 rad to +1000rad. By default, it plots from -2Π to +2Π rad

1. Unit Impulse  (aka Dirac delta): use f=dirac(x) => gives o/p=1, i.e a dc plot with value=1 at all x.

2. Sine wave: use f=sin(2*pi*x); => gives o/p as Π(-i)(dirac(w-2Π) - dirac(w+2Π)), since dirac func is infinite at +2Π and -2Π and 0 elsewhere, we just see 0 everywhere

3. Cosine wave: use f=cos(2*pi*x); => gives o/p as Π(dirac(w-2Π) + dirac(w+2Π)), again we just see 0 everywhere

2. Square signal: use f = rectangularPulse(a,b,x). Here a=starting of high pulse, b=end of high pulse. By default, if no a or b provided, i.e rectangularPulse(x), then a=-1/2, b=+1/2

syms x;
f=dirac(x);
FT = fourier(f);
ezplot(FT,[-1000,+1000]);

 

 

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Published: Thursday, 19 September 2019 16:13
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