Units of the vertical axis(frequency) in a fft-based-spectrogram

[ClaudioPedrazzi]

Hi everyone,

I need help for a really simple question, I bellieve, concerning the units in a spectrogram, that in turn comes from a fft function. I refer to the example to be found in QuickSheets "WAV-Files, Spectrograms and Signal Generation" (under Engineering Applications). Since I am not very confident with signal analysis, I have always problem to interpret the units in the frequency axis of an fft. In this example Quicksheet (also attached), the frequency axis is vertical as usual for spectrograms. But how can I know which frequency corresponds to the index of the plot?

For example: here I have 256 samples and the rows of "spectra" are 129. How do I convert this 129 in Hz? Which frequencies dominate in the signal in the first two seconds?

Here under I have now, as a test, only the half of the samples (128). The index is now 65. How do I convert this 65 in a frequency in Hz?

I can see that there is a proportionality, and that it must depend on the sampling rate and maybe on the total number of time points (also known), but I am unsure how to write a formula. As I said, it must be simple enough, but my background is more in the direction of structural mechanics!

Thanks a lot for any hint!

Regards

Claudio

[RichardJ · Accepted solution]

After the fft the lowest frequency is always 0 and the highest frequency is half the sampling rate (Nyquist theorum).

[ClaudioPedrazzi]

Thanks a lot!! I knew it had to be easy! So in this quicksheet the sampling rate is 20000, the "top line" of the spectrogram represents 10 kHz.

In the meantime I was able to confirm this comparing the spectrogram (of my real problem) with another spectral analysis made with hardware.

Best reagards

Claudio