2021 IEEE International Conference on Acoustics, Speech and Signal Processing

6-11 June 2021 • Toronto, Ontario, Canada

Extracting Knowledge from Information

2021 IEEE International Conference on Acoustics, Speech and Signal Processing

6-11 June 2021 • Toronto, Ontario, Canada

Extracting Knowledge from Information
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Paper Detail

Paper IDSPTM-22.5
Paper Title EIGENVECTORS OF ORDINARY, GENERALIZED, CENTERED AND OFFSET DISCRETE FOURIER TRANSFORMS BASED ON LOOKUP TABLE METHODS: EFFICIENCY AND APPROXIMATION USES
Authors Wen-Liang Hsue, Chung Yuan Christian University, Taiwan
SessionSPTM-22: Signal Processing Theory and Methods
LocationGather.Town
Session Time:Friday, 11 June, 13:00 - 13:45
Presentation Time:Friday, 11 June, 13:00 - 13:45
Presentation Poster
Topic Signal Processing Theory and Methods: [SMDSP] Sampling, Multirate Signal Processing and Digital Signal Processing
Abstract In this paper, we first propose a methodology to construct an eigenvector of the N*N discrete Fourier transform (DFT) matrix from any eigenvector of the (k^2N)*(k^2N) DFT matrix, where k is a positive integer. Computing an N-point DFT eigenvector using the proposed method is very efficient, which requires only N(k-1) additions and no multiplications with a pre-stored lookup table of (k^2N)-point DFT eigenvectors. Similar efficient methods are also developed to compute N-point eigenvectors of other DFT-related transforms, including the generalized DFT (GDFT), centered DFT (CDFT) and the offset DFT (ODFT), from (k^2N)-point eigenvectors of their corresponding transforms or the DFT. As application examples, we apply the proposed methods to compute N-point DFT, GDFT, CDFT and ODFT eigenvectors, which are closer to samples of the continuous Hermite-Gaussian function (HGF) than existing N-point eigenvectors, from their corresponding (k^2N)-point eigenvectors. These improved N-point Hermite-Gaussian-like eigenvectors can be used to define fractional versions of the various N*N DFT transforms whose outputs are closer to samples of the continuous fractional Fourier transform than outputs of the corresponding existing fractional transforms. Finally, we perform computer experiments to verify the effectiveness and demonstrate applications of our proposed methods.