What do I gain from a spectral analysis at higher sample rates?

Question

Cristian and me are currently doing some experiments with analyzing samples at samplerates of 96kHz or 192kHz. My initial thought was how can you keep the LowestAnalyzedFreq although the window size gets  smaller. In fact when I analyze a sample at 96K I get a significant bass loss. I don't think there's a way around that other than raising the number of partials and therefore making the window bigger (unless you've cracked the time/frequency dependency of windowing?). Well, this is all no problem because that's just the way spectral analysis works, right?

But my second thought concerns the resolution of the analysis: When I look at the right channel (frequencies) I see that there's still a ramp kind of curve going on. Now imagine I analyze a 48K sample at 96K: Let's assume I do a 256 samp (LowestAnalyzedFreq 87 hz) analysis. Now I have 256 partials in the range of 0 - 48K (half sample rate). But my original signal only contained useful information in the range of 0 - 24K. So the amount of partials containing useful information is only 128. If I had analyzed it at 48K I would end up with 256 partials containing useful information. So actually to get the best results I should analyse at the original sample rate of my sample, right?

Thanks!

Answer 1

Yes, the best results are when you analyze at the same sample rate as your original sample.  You are correct that the window length is a fixed number of samples so it is a shorter duration in seconds (higher frequency) at higher sample rates.

Answer 2

You normally choose the frame size (fundamental frequency) to match the content, so if you use 48K or 96K you will still want the same window duration (fundamental frequency) so you have to use a window of twice the number of samples. So if your original signal was at 48k sample rate you gain nothing analysing at 96K and if your original sample is at 96K, I doubt you would hear any difference if you first converted it to 48K and then analysed it, but I've always said that 96Khz is the emperor new clothes in any case.