Can a FFT be recreated by performing STFT on the smaller time intervals and then summing them up. My doubt is that FFT is a usually a amplitude vs frequency data and STFT has a x-axis in units of time. Is it logical to sum up STFT's to get the FFT?
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\$\begingroup\$ "FFT is a usually a amplitude vs frequency" This is incorrect. It's a complex number vs frequency which means magnitude and phase are present. If you trust Wiki: "So the Fourier transform can be seen as a sort of phase coherent sum of all of the STFTs of x(t)." en.wikipedia.org/wiki/Short-time_Fourier_transform. I'm not sure how STFT is different than performing FFT on several smaller time intervals though. \$\endgroup\$– DKNguyenCommented Aug 4, 2022 at 15:48
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\$\begingroup\$ See this answer on dsp.ee. \$\endgroup\$– a concerned citizenCommented Aug 5, 2022 at 6:20
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Can a FFT be recreated by performing STFT on the smaller time intervals and then summing them up.
No.
The STFT loses no information, it's invertible. Until that is, you take the magnitude, which you typically do for a power versus frequency versus time graph, the normal output format for such things. Then you've thrown away half the information, and can't get back to either the FFT or the time domain.
You could invert a bunch of STFTs, before the magnitude operation, to get back to the time domain, and then FFT that.
