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.
Chirplets, one-sided discrete Laplace transform related to damped sinusoid representation. (Bluestein 1970; L. Rabiner, Schafer, and Rader 1969; L. R. 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.)
Windowing the DTFT
(Harris 1978; Cooley, Lewis, and Welch 1970; Rafii 2018)
(Narasimha, Ignjatovic, and Vaidyanathan 2002; Ignjatovic 2007, 2009; A. Ignjatovic, Wijenayake, and Keller 2018b, 2018a; Ignjatovic, Wijenayake, and Keller 2019)
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