https://scholars.lib.ntu.edu.tw/handle/123456789/310460
Title: | Generalized eigenvectors and fractionalization of offset DFTs and DCTs | Authors: | SOO-CHANG PEI JIAN-JIUN DING |
Issue Date: | Jul-2004 | Journal Volume: | 52 | Journal Issue: | 7 | Start page/Pages: | 2032-2046 | Source: | IEEE Transactions on Signal Processing | Abstract: | The offset discrete Fourier transform (DFT) is a discrete transform with kernel exp[-j2π(m - a)(n - b)/N]. It is more generalized and flexible than the original DFT and has very close relations with the discrete cosine transform (DCT) of type 4 (DCT-IV), DCT-VIII, discrete sine transform (DST)-IV, DST-VIII, and discrete Hartley transform (DHT)-IV. In this paper, we derive the eigenvectors/eigenvalues of the offset DFT, especially for the case where a + b is an integer. By convolution theorem, we can derive the close form eigenvector sets of the offset DFT when a + b is an integer. We also show the general form of the eigenvectors in this case. Then, we use the eigenvectors/eigenvalues of the offset DFT to derive the eigenvectors/eigenvalues of the DCT-IV, DCT-VIII, DST-IV, DST-VIII, and DHT-IV. After the eigenvectors/eigenvalues are derived, we can use the eigenvectors-decomposition method to derive the fractional operations of the offset DFT, DCT-IV, DCT-VIII, DST-IV, DST-VIII, and DHT-IV. These fractional operations are more flexible than the original ones and can be used for filter design, data compression, encryption, and water-marking, etc. © 2004 IEEE. |
URI: | http://scholars.lib.ntu.edu.tw/handle/123456789/310460 https://www.scopus.com/inward/record.uri?eid=2-s2.0-3142715345&doi=10.1109%2fTSP.2004.828904&partnerID=40&md5=011cadeab94ea196477579f093ee9191 |
ISSN: | 1053587X | DOI: | 10.1109/TSP.2004.828904 | SDG/Keyword: | Convolution; Cosine transforms; Cryptography; Data compression; Digital filters; Digital watermarking; Discrete Fourier transforms; Eigenvalues and eigenfunctions; Frequency domain analysis; Matrix algebra; Polynomials; Theorem proving; Commutative matrix method; Discrete cosine transforms; Discrete fractional Fourier transform; Hermite polynomial; Offset discrete Fourier transform; Digital signal processing |
Appears in Collections: | 電機工程學系 |
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