In signal processing, the Fourier transform is a popular method to analyze the frequency content of a signal, as it decomposes the signal into a linear combination of complex exponentials with integer frequencies. A fast algorithm to compute the Fourier transform is based on a binary divide and conquer strategy. In computer algebra, sparse interpolation is well-known and closely related to Prony’s method of exponential fitting, which dates back to 1795. In this paper we develop a divide and conquer algorithm for sparse interpolation and show how it is a generalization of the FFT algorithm. In addition, when considering an analog as opposed to a discrete version of our divide and conquer algorithm, we can establish a connection with digital filter theory.
CITATION STYLE
Briani, M., Cuyt, A., & Lee, W. shin. (2017). Sparse Interpolation, the FFT Algorithm and FIR Filters. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 10490 LNCS, pp. 27–39). Springer Verlag. https://doi.org/10.1007/978-3-319-66320-3_3
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