Some comments on taking a power spectra of a time series

matlab-macro.jpg

I have been noticing more and more the tendency of tutorials or help information on the fast Fourier transform (FFT) to completely ignore signal windowing/enveloping/tapering. The sample code typically starts out with generating a time series made up of one or more sinusoids with possible random noise included. The code then takes an FFT of the data and displays the power spectra. This simple method works well for a small class of signals whose properties are not changing over the time bin and whose values go to zero at the start and end of the time bin. In all other cases, more about
there is some degree of spectral leakage, overweight
or unnecessary broadening of spectral peaks and potential additional spectral noise. The typical solution to this problem to subdivide the whole time series into overlapping time-bins and then apply some kind of window function and only then perform a FFT. Care should be taken to normalize the resulting FFT with the area of the window function so that accurate power values are preserved. Things get more complicated if the time series under analysis deals with point processes, viagra 100mg
something which may be described later. The image above is a μblog original and may be used freely.

( an014-understanding-fft-windows.pdf )

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