# frequency components of discrete Gaussian-windowed signal

When we are do a discrete Gabor transform on a 1D signal, we apply a Gaussian window on a segment of the signal. However, due to the tapering ends of the Gaussian window, the magnitude of the data points will be reduced more towards the ends, This implies that the the frequency components of the segment of the signal will be suppressed when we apply FFT to it. After performing some experiments, I found that at least 2 periods of the signals is required, so that no misjudgement of the behaviour of the signal will happen.

What is the range of frequencies in which the magnitude of the FFT is still representative of the frequencies of windowed signal?

• The opposite of frequency suppression. The narrower the Gaussian window on a stationary signal, the wider the bandwidth of each Gabor filter. – hotpaw2 Nov 18 '13 at 16:01
• How do we prove this? @hotpaw2 – meta_warrior Nov 18 '13 at 16:04

The table says there is a processing gain of $0.37$ to $0.51$ depending on your $\alpha$ parameter: