Questions Regarding Time Resolution & Input Signal Length

[cwitkowitz]

Hi @eloimoliner,

Thank you for this implementation of CQ-NSGT. I would like to use it as a drop-in replacement of the more standard CQT implementation, but I am confused on several points:

• I am having trouble developing an intuition for the precise location in time that each coefficient corresponds to. Is there a way to compute these values? For the standard CQT, this is trivial, since each coefficient corresponds to the dot-product of each basis at user-defined intervals of hop_length. However, I cannot figure out from the CQ-NSGT code how one would go about determining the analogue to this concept, or if one even exists (i.e., does time resolution depend on signal length?). A similar question was raised here, and the advice of simply dividing the input signal length by the number of coefficients was given. But then is there some offset from t=0 for the first coefficient?

• Given that signal length is a parameter to the CQ-NSGT implementation, I am wondering if anything fundamental changes about the coefficients when the signal length is changed. What exactly depends on the signal length of the input signal, and would coefficients based on one signal length be comparable to coefficients based on another, even if the two signal lengths are very different (e.g., 10 s vs. 100 s)?