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Recently I learned that the DFT has good numerical stability since it can be represented as an orthogonal matrix, which has a condition number of 1.

Is it possible to represent the STFT and DWT as matrices and asses their numerical stability using condition numbers?

To be specific and capable of comparing stability between STFT and DWT, the wavelet would need to be a sinusoid as shown here (also should have an imaginary portion):

enter image description here

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  • $\begingroup$ Which DWT? Stfts are implemented by dfting a windowed signal so your results have to be window dependent. $\endgroup$
    – Batman
    Dec 26 '14 at 2:35
  • $\begingroup$ I think, for accurate comparison, the wavelet would need to be a sinusoid as well. Also is there no window that yields the lowest condition number for STFT? $\endgroup$
    – Malz
    Dec 26 '14 at 6:53

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