Q354 : Purpose of Sampling Exponent

Question
How can I select a proper sampling exponent in FFTSES?

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Answer
The "Sampling Exponent" acts in concert with the "Time Duration" field to define several quantities: the time resolution, the frequency resolution, the total time duration and the largest frequency being sampled. The "Lightning.pdf" HowTo document gives a pretty good description of the criteria to use when selecting a "Sampling Exponent" and a "Time Window". The relevant paragraph is reproduced below.

"The width of the time window T and the number of sampling points N are the two important quantities for digitizing the time domain signal. The first criterion for choosing T is that the signal should become substantially smaller for times greater than T. The second criterion is that T should be sufficiently large for the fundamental frequency (or frequency step) f = 1/T to be small enough to detect any resonance peak that might be present in the frequency domain system response. The second criterion is usually unknown until the frequency domain system responses are computed. Once T is determined, N should be chosen for the time interval t = T/N to be small enough to resolve all the features of the time domain surge signal."

In the above paragraph, N is equal to 2^{Sampling Exponent} and T is equal to the "End Time Duration" on the FFTSES Computations screen for Forward FFT. To this, I would add that the parameters should be chosen so that the modulated response be very small at the largest computation frequency, which is given by N/T.

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