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Multiplication in the frequency domain is equivalent to circular convolution in the time domain with a period of NFFT. If you don't zero pad them to at least length(x1)+length(x2)-1 samples, the IFFT result would be aliased in the time domain. That's why overlap-save method discards part of the result.


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It's the spectrum of a discrete signal: sampling in time $\Leftrightarrow$ periodizing in frequency - explained in detail here. Overlap means there's aliasing, and we require a higher sampling rate. FFT returns one period of this spectrum since it contains all the information. (More precisely, your image shows DTFT, and DFT (which FFT implements) is a ...


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It barely matters – speech has no significant content close to 12 kHz, so using a relaxed filter works. Reduce the filter steepness a lot; as long as things up to 6 kHz pass through, you won't hear a difference.


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In essence you are trying to build an audio synthesizer that creates sounds with a given pitch. Over the last 50 years there have been dozens of technologies developed to do this: you can start here with an overviews: https://en.wikipedia.org/wiki/Synthesizer To get reasonably natural sounding instrument sound, your best bet is probably to build a sample ...


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Is this normal? Yes. The way you call periodogram() it simply does a single FFT of the entire vector and squares the result to get the power. The mean of your vector is about 150 and it's 24000 sample long, i.e. the FFT at DC is 24000*150. When you square this you get something in the order of $13\cdot 10^{12}$. periodogram() also scales to spectral density ...


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