Discrete time Fourier and related transforms

Also, chirplets, z-transforms, chromatic derivatives…

Care and feeding of Discrete Fourier transforms (DTFT), especially Fast Fourier Transforms, and other operators on discrete time series. Complexity results, timings, algorithms, properties. These are useful in a vast number of applications, such as filter design, time series analysis, various nifty optimisations of other algorithms etc.

Chirp z-transform

Chirplets, one-sided discrete Laplace transform related to damped sinusoid representation. (Bluestein 1970; Rabiner, Schafer, and Rader 1969)

A recent publication (Sukhoy and Stoytchev 2019) shows that these are as tractable as FFTs to invert, which is to say, very. I will read the paper and see if that is as useful to me as it seems like it might be, (The paper has a lot of elementary proofreading errors, which is a bad start.)



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———. 2018b. Chromatic Derivatives and Approximations in Practice—Part II: Nonuniform Sampling, Zero-Crossings Reconstruction, and Denoising.” IEEE Transactions on Signal Processing 66 (6): 1513–25.
———. 2019. “Chromatic Derivatives and Approximations in Practice (III): Continuous Time MUSIC Algorithm for Adaptive Frequency Estimation in Colored Noise,” 16.
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