What are the invertible (preferably linear) representations of an audio/speech signal which captures the essence of signal in different resolutions and details. Basically, I am looking for Laplacian/Gaussian pyramid, not for images, but for audio signals. The interesting aspect of it for me is that it keeps the coarse-level perceptual details and gradually fills in the fine-level perceptual details.

  • $\begingroup$ You can just use 1-D Gaussians, the same properties basically apply. $\endgroup$ – geometrikal Jun 29 '15 at 4:26
  • $\begingroup$ You are asking "what are" before asking if they exist. You might want to first ask if any pyramid exists that is invertible (and perhaps orthogonal and complete as well). Or if you only want to capture the "essence", perhaps you don't want or need invertibility. $\endgroup$ – hotpaw2 Jun 29 '15 at 16:28
  • $\begingroup$ @hotpaw2 I definitely need invertibility, in addition to representing the signal as multiple levels of resolution. As geometrikal proposed, 1-D Gaussian is a potential option. I am looking for other options to compare the performance of my application, and quality of synthesized signals. $\endgroup$ – Soroush Jun 29 '15 at 22:21

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