Finally a teacher who could explain this concept CLEARLY. Very very very thanks Mr. Van Veen. Teaching something to someone and comprehending what it is are completely different SKILLS. Not everyone should be allowed to be teacher! Thanks again sir!
The continuous-time version of this result is shown in Lecture 9 of the Introduction and Background playlist, "Properties of Fourier Transforms", starting at about 9:15. The specific case of an impulse train is an example used to illustrate finding the FT for periodic signals. The DT case is very similar. I can't recall at the moment if I show the DT version anywhere. Let me know if this doesn't answer your question.
Is there a rule on what the time index values should be? For example, if I want to take the DFT of x(n) = cos(n) with a window of n = 0, 1, 2? Can I just sample once per second?
I don’t know what’s going on and what you meant, but when you plug in a function to the inverse function you get the original value, alas x[n] and by no means you shall omit the formula of the sum of DFT from calculation of the inverse function. x[n] shall be a signal, but it turns to be the frequency domain for your calculation in DFT and it falls apart to be the signal - same x[n] for your calculation in DTFT. I hope I don’t distract the learning process for anyone, but someone who wrote about Fourier Series on Wikipedia in my native language has already succeeded to confuse 1000 EE students, so just watch ahead. I was wondering why such a good video has 28 dislikes, though I found out the source of the downvotes. Thanks though for working hard in explaining, the first 2.5 minutes indeed helped.
The DFT is sometimes called a discrete-time Fourier series, but in the signal processing field it is more common to use the name DFT. I agree it is not the "best" terminology, but it is established now and would be pretty difficult to try to change it.
I wish someday that Artificial Intelligence Engineering Physics mathematical Software will make a real world computerized simulation/animation with the aid of high tech 'SPECTRUM ANALYZERS / Vector Network Analyzers, of this type of too much complex topic to understand.
Dear Barry I need to calculate heart rate variability by using fast Fourier transformation and find total power and High frequency and Low frequency. ex) x=[0.465,0.466,0.470,0.500] How can I do that for above example.
Hmm, I'm not sure I understand your question. Specific questions like this are often appropriate for the "signal processing stack exchange" forum. RU-vid won't let me post the url, but if you google what I put in quotes you should find it easily. But you will have to give more details about your problem so people can understand it. Good luck.
