Why do Periodic Signals have Discrete Frequency Spectra? 

Thanks for the suggestions, I don't have much on coding at the moment. I'll put these topics on my "to do" list. You can check out all my videos in categorised listing at iaincollings.com I've got a basic video on convolutional coding, and some on decoding: "What is a Convolutional Code?" ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-EgYKMDBj_zQ.html and "Decoding Convolutional Codes: The Viterbi Algorithm Explained" ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-IJE94FhyygM.html

It's great to hear you've found the videos helpful!

Glad it was helpful!

Thanks. It's great to know that people like the videos.

Thanks for your nice comment. I'm glad you like the videos.

Thanks. Glad you like the videos.

Glad it was helpful!

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

I'm glad you found it useful.

Yes, that's one way to put it. Here's a video showing what you've said: "Visualising the Fourier Transform" ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-U7ii8agAhIs.html

And what does the phase look like of periodic signals by the way, that's not discrete is it?

I think you're confusing things. You say that "when we deal with signals that are time limited, we should see in the spectrum a series of sincs, centered around multiples of 1/T" ... but that's not true. Signals that are time-limited have a spectrum that is frequency-unlimited. eg. the rect function has a Fourier transform that is a sinc, that goes from negative infinity to positive infinity ... but it doesn't repeat. You seem to be mixing this up with the situation when signals are time-sampled with a sampling period T - then their frequency response repeats at 1/T. You can find many videos on my channel related to sampling, and also to the Fourier transform of rect. A full categorised listing can be found here: www.iaincollings.com/signals-and-systems

@@iain_explains why doesn't the sinc repeat? If I apply a rectangular window, ie I multiply it in the time domain, that'd be convolving in the frequency domain with the transform of the periodic signal, that is discreet

Which sinc are you talking about? Maybe this video will help: "Visualising the Fourier Transform" ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-U7ii8agAhIs.html

Glad it was helpful!

Well, I'd say that the best way is to be curious, and always ask yourself "What", "How" and "Why", and if that doesn't get you the answer, then check out the videos on my channel 😁

Yes, that's right.

So, the DC value can be calculated directly as an average in time-domain, without resorting to a DFT. (with proper scaling "2pi" based on the Fourier transform definition that has been used).