Hi all! I hope this is the right subcategory to ask in. I’m playing around with the FFTW package to perform some Fourier transforms. I got how to define a signal and transform it, but I can’t get how (and why) can I shift the frequency domain to reflect the actual frequencies of my signal. My Googl…

[image] bertulli: since the original signal had frequency = 1? The original signal repeats how many times per 100 samples? It’s 100/(2pi) ~16 Time is measured by the duration of the sample… Frequency is measured by cycles per duration of sample If you want to calculate with physical frequen…

[image] bertulli: the original signal had frequency = 1 If the original angular frequency is 1, to get it we have to multiply fftfreq() by 2π. See annotated code below: using FFTW, Measures, Plots; gr() x = 0:100 N = length(x) y = sin.(x) # ω0*x = x; with angular frequency ω…

Uhm, I think I see the problem but I can’t understand the solution: what frequencies does the DFT outputs? Radians? If this is so, shouldn’t I get the “right” frequencies in the output (and graph) without calling fftfreq (since sin.(x) also expects radians)?

[image] bertulli: what frequencies does the DFT outputs? Cycles per window length.

[image] bertulli: fftshift(fftfreq(length(x)) * length(x)) Give the sample freqiency as the second argument to fftfreq, and do not multiply by length(x). I usually do something like this to get it right: using FFTW using UnicodePlots let fs = 1000 # sample freq duration = 1 time…

[image] bertulli: what frequencies does the DFT outputs The DFT assumes the input data is periodic and it outputs amplitudes of the sinusoids whose frequencies are defined as a multiple of a fundamental frequency that is equal to the inverse of the input data duration (called also fundamental…

I think I’m slowly getting now. I think I misunderstood some quirks of the DFT, and the problems that arise in the sampling process. For instance, I now get that the DFT has no way of teling what the frequencies were, if you don’t take into account the sampling frequency. That iiuc it’s the reason w…

[image] bertulli: I now get that the DFT has no way of teling what the frequencies were There is no need to define physical units in the mathematical definition of FFT, as hinted in my previous post. However, the main applications of FFT are in engineering where physical units of time or spac…

Many thanks! I think I’m getting it now. :+1: One more thing: in Julia, which is is the coefficient of the DFT? The unitary one (1/\sqrt(N))? And why? (I can open a new topic if this is too OT)

How do frequencies shift after a FFT?

Specific Domains Signal and Image Processing

stephancb October 5, 2022, 11:56am 5

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How do frequencies shift after a FFT?

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