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I have to compare the compression capacity of different transformations on the same signal. The explanations were very brief, but i have to compare some energy thresholds(e.g. 50% of the total energy) in terms of the number of coefficients containing that energy. We were only shown a graph of Spectral Power over normalized frequency.

It's unclear to me how to go about comparing these transforms. Isn't the Spectral Power an FFT of that signal? Do i have to compute the DCT and then do an FFT over the resulting signal? Also, how do i determine how mant points contain a certain amount of energy?

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  • $\begingroup$ Is the goal to maximize the energy compaction, or is it ok to have potentially long zero-runs, or to be able to quantize harshly without too much perceived distortion? $\endgroup$
    – Knut Inge
    Jan 14, 2022 at 14:50
  • $\begingroup$ @KnutInge i only have to compare the compression of already performed transformations. To be concise, i have to compare Hotelling Transform with Discrete Cosine Transform for the same signal in term of how much energy is contained in what number of samples (for example, looking at what number of samples contain 90% of the energy for both transforms). We were shown just a plot of spectral power over normalized frequency. $\endgroup$
    – conopizda2
    Jan 15, 2022 at 12:26

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I always thought an interesting comparison would be the autocorrelation result of the transformed signal. This goes on the assumption that the closer the resulting signal is to white noise, the better the compression is as it has effectively removed all memory (redundancy) from the signal. That said, white noise has an autocorrelation function that is an impulse (with the autocorrelation at $\tau=0$ equal to the variance of the signal). So an interesting metric would be the width of the normalized (divide by the variance) auto-correlation functions which I suspect would be consistent with the effectiveness of the transforms in removing redundancy/memory, at least to the extent that redundancy is linearly related.

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