Signal compression using discrete fractional Fourier transform and set partitioning in hierarchical tree

Signal compression has been characterized as the removal of redundancy and irrelevancy. Fractional Fourier Transform (FRFT), an orthogonal, linear transform, is known to decompose the signal in terms of chirps. In this paper we propose a scheme for signal compression based on the combination of discrete FRFT (DFRFT) and set partitioning in hierarchical tree (SPIHT). The application of the scheme to different types of signals demonstrates significant reduction in bits leading to high signal compression ratio. The results are compared with those obtained with discrete cosine transform (DCT).

[1]  Bryan Usevitch,et al.  A tutorial on modern lossy wavelet image compression: foundations of JPEG 2000 , 2001, IEEE Signal Process. Mag..

[2]  L. Cohen,et al.  Time-frequency distributions-a review , 1989, Proc. IEEE.

[3]  James H. McClellan,et al.  The discrete rotational Fourier transform , 1996, IEEE Trans. Signal Process..

[4]  Soo-Chang Pei,et al.  Fractional Fourier series expansion for finite signals and dual extension to discrete-time fractional Fourier transform , 1999, IEEE Trans. Signal Process..

[5]  Chien-Cheng Tseng,et al.  A new discrete fractional Fourier transform based on constrained eigendecomposition of DFT matrix by Lagrange multiplier method , 1999 .

[6]  Luís B. Almeida,et al.  The fractional Fourier transform and time-frequency representations , 1994, IEEE Trans. Signal Process..

[7]  Bor-Sen Chen,et al.  A multi-input-multi-output system approach for the computation of discrete fractional Fourier transform , 2000, Signal Process..

[8]  Alfred Mertins,et al.  FROM LOSSY TO LOSSLESS AUDIO CODING USING SPIHT , 2002 .

[9]  F. Hlawatsch,et al.  Linear and quadratic time-frequency signal representations , 1992, IEEE Signal Processing Magazine.

[10]  Soo-Chang Pei,et al.  Closed-form discrete fractional and affine Fourier transforms , 2000, IEEE Trans. Signal Process..

[11]  Soo-Chang Pei,et al.  A novel method for discrete fractional Fourier transform computation , 2001, ISCAS 2001. The 2001 IEEE International Symposium on Circuits and Systems (Cat. No.01CH37196).

[12]  Gozde Bozdagi Akar,et al.  Digital computation of the fractional Fourier transform , 1996, IEEE Trans. Signal Process..

[13]  Chih-Lung Lin,et al.  A quality-on-demand algorithm for wavelet-based compression of electrocardiogram signals , 2002, IEEE Transactions on Biomedical Engineering.

[14]  William A. Pearlman,et al.  A new, fast, and efficient image codec based on set partitioning in hierarchical trees , 1996, IEEE Trans. Circuits Syst. Video Technol..

[15]  Z. Zalevsky,et al.  The Fractional Fourier Transform: with Applications in Optics and Signal Processing , 2001 .

[16]  Martin J. Bastiaans,et al.  On fractional Fourier transform moments , 2000, IEEE Signal Processing Letters.

[17]  Chien-Cheng Tseng,et al.  Discrete fractional Fourier transform based on orthogonal projections , 1999, IEEE Trans. Signal Process..

[19]  Vivek K. Goyal,et al.  Theoretical foundations of transform coding , 2001, IEEE Signal Process. Mag..