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http://hdl.handle.net/1893/28262| Appears in Collections: | Computing Science and Mathematics Conference Papers and Proceedings |
| Author(s): | Briani, Matteo Cuyt, Annie Lee, Wen-shin |
| Contact Email: | wen-shin.lee@stir.ac.uk |
| Title: | Sparse interpolation, the FFT algorithm and FIR filters |
| Editor(s): | Gerdt, VP Koepf, W Seiler, WM Vorozhtsov, EV |
| Citation: | Briani M, Cuyt A & Lee W (2017) Sparse interpolation, the FFT algorithm and FIR filters. In: Gerdt V, Koepf W, Seiler W & Vorozhtsov E (eds.) Computer Algebra in Scientific Computing - 19th International Workshop, CASC 2017, Beijing, China, September 18-22, 2017, Proceedings. Lecture Notes in Computer Science (LNCS), 10490. 19th International Workshop on Computer Algebra in Scientific Computing, Beijing, China, 18.09.2017-22.09.2017. Cham, Switzerland: Springer International Publishing, pp. 27-39. https://doi.org/10.1007/978-3-319-66320-3 |
| Issue Date: | 31-Dec-2017 |
| Date Deposited: | 3-Nov-2018 |
| Series/Report no.: | Lecture Notes in Computer Science (LNCS), 10490 |
| Conference Name: | 19th International Workshop on Computer Algebra in Scientific Computing |
| Conference Dates: | 2017-09-18 - 2017-09-22 |
| Conference Location: | Beijing, China |
| Abstract: | 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. |
| Status: | VoR - Version of Record |
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