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What I'm doing is that I send an audio signal consisting of a single frequency into a resonator. To check whether and how the signal has changed I perform a QAM demodulation.

I do not need intend to recover the signal or something like that, I'm just interested in the magnitude of the change/modulation of the input signal.

In the next step I would like to use multiple frequencies simultaneously and analysed how the amplitude of each signal has changed.

Is there a different/better way than just analysing the signal by Fourier transform?

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Well, you can of course instead of using the Discrete Fourier Transform as filter bank just employ bandpass filters to extract your individual tones.

(The DFT is really just a filter bank, if you think about it: it correlates an input sample vector with different complex oscillations. Which is convolution with their conjugate time inverse, which is a filter operation.)

This might be advantageous, since the filter shape of a DFT is inherently sinc-shaped, which I guess isn't quite close to what you want in terms of spectral sidelobes.

So, yeah, simply design a narrow low-pass filter, and shift it in frequency to the appropriate position. (Do that for every tone.).

If you've got many tones that you space on a regular grid, you might want to do a polyphase filter bank, but I'd consider this an "advanced computational optimization that you probably don't need in your measurement process, as you don't care whether computations take a milli- or 100 microsecond".

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  • $\begingroup$ Thanks for your answer. But it opens another question, as filters are applied by convolutions (as far as I know, correct me if I'm wrong) I still have to perform a DFT. Do I, therefore, face the same issue as by just using the DFT in the first place? $\endgroup$
    – Stanissse
    Feb 15, 2021 at 20:08
  • $\begingroup$ no, not really. In the first place, you're using the DFT as the filter. In the second case, you're using many DFTs just as an algorithmic means to implement a different filter (you don't have to use the DFT to do a convolution. It's just an elegant ways to get there.). $\endgroup$
    – Marcus Müller
    Feb 15, 2021 at 22:08

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