I had preliminary knowledge of digital signal processing from Oppenheim's Discrete-Time Signal Processing and is studying time-frequency analysis now. May someone suggest introductory reference (textbook, website, review paper...) for the fast algorithm aspects of time–frequency analysis?


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If you are interested in discrete linear systems (either time-frequency or time-scale), you could invest in multirate filter banks, that provide tools for computing, optimizing, etc, such as the polyphase matrix or the lifting scheme. A tutorial paper is

An earlier reference is

However, additional notes could be helpful on you side whether you need:

  • specificities: amount of memory, real-time constraints, quantization
  • analysis only or analysis/synthesis
  • linear or nonlinear time-frequency
  • discrete or discrete approximation to continuous
  • fast in number of operations, convergence, or using hardware capabilities (finite-precision, approximate versions, etc.)

If you do consider sliding windows for Fourier analysis, this can be cast into the framework of modulated complex oversampled filterbanks, for which fast algorithms do exist, see for instance:

  • $\begingroup$ The reference is very useful. Thank you. I am looking for analysis only, linear time-frequency, discrete, fast in number of operations algorithm. The specificities is quite arbitrary as I am a greenhorn and is now focusing on the basic part of fast algorithm. $\endgroup$
    – Rikeijin
    Commented Sep 15, 2017 at 10:13

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