Why are Sinc and Square a Fourier Transform Pair?

Iain Explains Signals, Systems, and Digital Comms

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An intuitive explanation of the relationship between the rectangular (Rect) function and the Sinc function, in Fourier transforms. The video includes Matlab plots to illustrate the Fourier construction. The code for the plots can be found at www.iaincollings.com
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For a full list of Videos and accompanying Summary Sheets, see the associated website: www.iaincollings.com

Опубликовано:

30 апр 2023

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Комментарии : 21

@Pipolag1 9 месяцев назад

Great videos Iain! I've never seen this explained so clearly. Thanks so much.

@iain_explains 9 месяцев назад

Thanks. I’m glad you liked the explanation.

@floretionguru2977 Год назад

Great explanations of a difficult topic- good job!

@iain_explains Год назад

Thanks. I'm glad you liked it.

@sugatabhunia3368 Год назад

Sir ,can u please consider making some videos on the technicalities of Terahertz communication for B5G/6G applications.. it would be of great help !!

@iain_explains Год назад

Thanks for the suggestion. It's on my "to do" list.

@amitpalkar934 Год назад

Excellent and intuitive explanation

@iain_explains Год назад

I'm glad you liked it.

@mariahybinette5376 7 месяцев назад

Nice visuals, for exlaining!

@iain_explains 7 месяцев назад

Glad you like them!

@ehabdawood7708 Год назад

Thanks, amazing video.. ❤

@iain_explains Год назад

Glad you liked it.

@maazawan7629 11 месяцев назад

Sir first of all thank you for a very useful and insightful video. In the end, you said that the sum of areas of delta impulses is equal in all 3 cases but at the same time we know that for a square wave with an infinity period will have more ipulses with each impulse having a smaller area and smaller contribution in the overall sum....how can that be shown? You implied it and I agree but there must be a way to visualize that as well

@iain_explains 11 месяцев назад

I'm not sure what you mean. What do you mean when you say "for a square wave with an infinity period will have more pulses"? What "more pulses" are you talking about? If the period is infinity, then there is only one "pulse".

@maazawan7629 11 месяцев назад

@@iain_explains sorry sir...amend to read "sum of areas of deltas impulses is equal in all 3 cases"

@pitmaler4439 Год назад

Splendid, many thanks. Perhaps it is worthy to do a single video about MMSE. You refer very often to it and it is important in communications theory. Obviously, there is a linear and a non linear version. (Where is it used in communication? Do we just need the linear version? Derivation)

@iain_explains Год назад

Thanks for the suggestion. I've put it on my "to do" list.

@power-max Год назад

Doesn't phase also matter when constructing a superposition of a whole bunch of sine waves to make the square wave? Could one argue that you could simply shift 2/2T over a bit so the edges align? Pretty sure I could, but in doing so only some edges would line up while others won't (answering my own question).

@iain_explains Год назад

Yes, you're right - phase does matter. But in this case, the square waveform is symmetric around t=0, and the only sinusoid that matches that property is the cos wave with zero phase offset (or the negative cos wave - which is the positive cos wave with 180deg phase offset). So at each frequency, the (Fourier) component will be a cos wave with a +/-1 multiplier.

@svaditya2896 Год назад

Excellent explanation. My question is: Applying the same procedure that you did for 1/T( Checking for gradient at that point for every contribution), for 2/T frequency of the Sinc wave, then there will be twice the number of frequency components ( for the 1/4 case for example, we have to calculate until 8/4T), and hence is it right to ignore this part when we express it as a rect function? I understand that the contribution of the constant decreases as we increase frequency, but can we neglect these sidelobes of sinc function completely?

@iain_explains Год назад

Sorry, I don't understand what you're asking. I didn't neglect any of the sidelobes.