This question is derived by this question and the corresponding answer. The problem was that I had a $sech(x)$-function in a specific time interval, and I applied a fft on it. But when I increased the amount of points in the time interval, the resulting function got narrower. The answer was that I am shifting the original function to higher frequencies (by keeping it at the same width), and therefore reducing the size of the fft-result.
As far as I know, that is not correct. Is there a mathematical explanation why I get a narrower fft-function when I am increasing the amount of points in the time interval, but keeping the FWHM of the original function constant?
2026-05-16 15:53:45.1778946825
Increasing the points in a time scale changes the shape of the fft-function
93 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail At
1
The fourier transform of your function has not gotten narrower. It is exactly as it was before. You simply have appended more empty space to the size because the frequency bandwidth is limited.
Addition: If you expand the time interval, the frequency domain will get denser. If sample the same time interval more densely, the frequency domain will expand.