4 ms·
The "integration to zero" effect the author observes is a consequence of the fact that the Fourier Transform is meant only for periods signals. Practically, we
by thatcherc 4y ago
The "integration to zero" effect the author observes is a consequence of the fact that the Fourier Transform is meant only for periods signals. Practically, we all often toss any time series data into an FFT to get a look at it in frequency space, but the math is only exactly correct with the time series samples used from one cycle of a period signal that repeats forever.
By generating the frequency domain Fourier coefficients and then transforming them to the time domain, the author is guaranteed to get a signal that starts and ends at the same value, because the transformation assumes it's a periodic signal and so the first and last values of the period must be the same.
- dls2016 4y agoAlso, it seems like the author might not be aware that the FT of a Gaussian is another Gaussian. I implemented this method (Timmer and Konig) a few months ago, and I think there are some other statistical tricks that work out nice for Gaussians.
- ssfrr 4y agoThe author identified the cause of the integration-to-zero behavior - they've set the DC (0Hz) component to 0, so the signal must sum to 0. Any length-N signal can be thought of as one period of an N-periodic signal, so the FFT will be exact. It's not the first and last samples that need to be identical, it's the 1st sample needs to match the (N+1)th sample (1-indexed), which comes right after the last sample of the original finite signal. For example if you have the length-8 signal 12345678, the FFT is valid - you can think of it as a slice of the signal ...123456781234567812345678...