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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Chromatic derivatives
(Narasimha, Ignjatovic, and Vaidyanathan 2002; Aleksandar Ignjatovic 2007; A. Ignjatovic 2009; Aleksandar Ignjatovic, Wijenayake, and Keller 2018b, 2019, 2018a)
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References
Antoniou, Andreas. 2005. Digital Signal Processing: Signals, Systems and Filters. New York: McGraw-Hill.
Bluestein, L. 1970. “A Linear Filtering Approach to the Computation of Discrete Fourier Transform.” IEEE Transactions on Audio and Electroacoustics 18 (4): 451–55. https://doi.org/10.1109/TAU.1970.1162132.
Box, George E. P., Gwilym M. Jenkins, Gregory C. Reinsel, and Greta M. Ljung. 2016. Time Series Analysis: Forecasting and Control. Fifth edition. Wiley Series in Probability and Statistics. Hoboken, New Jersey: John Wiley & Sons, Inc.
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Hassanieh, H., P. Indyk, D. Katabi, and E. Price. 2012. “Simple and Practical Algorithm for Sparse Fourier Transform.” In Proceedings of the Twenty-Third Annual ACM-SIAM Symposium on Discrete Algorithms, 1183–94. Proceedings. Kyoto, Japan: Society for Industrial and Applied Mathematics. http://groups.csail.mit.edu/netmit/sFFT/soda_paper.pdf.
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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. https://doi.org/10.1109/TSP.2017.2787149.
———. 2019. “Chromatic Derivatives and Approximations in Practice (III): Continuous Time MUSIC Algorithm for Adaptive Frequency Estimation in Colored Noise,” 16.
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