I am familiar with the spectral leakage problem in FFT due to a rectangle window for a sin signal giving two peaks that leak to each other. My question is will the leakage to the frequency bins near the peaks increase if the peaks are closer to each other?
2 Answers
$\begingroup$
$\endgroup$
Sort of. The leakage has the shape of a Dirichlet Kernel. This similar to a sinc shape so the leakage diminishes with distance. However there is a significant fine structure so it's not monotonic.
$\begingroup$
$\endgroup$
It's not exactly leakage. If the frequency of interest contains an integer number of cycles, its peak lands right on one of the frequency domain samples, and its nulls land on the others, creating an ideal result (images borrowed from https://wirelesspi.com/dft-examples/)
However, any frequency in between the points defined by the sampling rate and window will not line up so precisely, so the peak will fall between samples and the other lobes will have a detectable effect on other output samples.
This seems to be leakage, but it's a side effect of attempting to represent a continual signal with discrete samples.
If you increase the number of samples in a window, you will have more output points and the sinc function not only oscillates faster, but decays faster as it gets farther from the center frequency.
