论文信息 - Input-output gains of linear periodic discrete-time systems with application to multirate signal processing

Input-output gains of linear periodic discrete-time systems with application to multirate signal processing

Two input-output gains of linear periodically time-varying (LPTV) systems are defined, namely, G(l/sub 2/, l/sub 2/)-the worst-case l/sub 2/ norm of the output over all inputs of unit l/sub 2/ norm-and G(RMS, RMS)-the worst-case RMS value of the output over all inputs of unit RMS value. It is proved for LPTV systems that these two gains are equal, a known fact for LTI systems. In addition, the relationship between two recently introduced generalized frequency responses for LPTV systems is derived. Finally, M-channel maximally decimated filter banks are considered, where, except in the ideal case of perfect reconstruction, aliasing distortion, magnitude distortion, and phase distortion are present. It is shown how these are kept small if the filter bank is designed by a method that optimizes the gain G(l/sub 2/, l/sub 2/) of an error system.

B. Francis | Tongwen Chen | S. Mirabbasi

[1] W. A. Brown. On the Frequency Response of Sampled-Data Systems , 1969 .

[2] Yutaka Yamamoto,et al. New approach to sampled-data control systems-a function space method , 1990, 29th IEEE Conference on Decision and Control.

[3] P. Vaidyanathan. Multirate Systems And Filter Banks , 1992 .

[4] Bassam Bamieh,et al. A general framework for linear periodic systems with applications to H/sup infinity / sampled-data control , 1992 .

[5] Tomomichi Hagiwara,et al. Frequency-response of Sampled-data Systems II: Closed-loop Consideration , 1993 .

[6] Pramod P. Khargonekar,et al. Frequency response of sampled-data systems , 1993, Proceedings of 32nd IEEE Conference on Decision and Control.

[7] Thomas W. Parks,et al. Linear periodic systems and multirate filter design , 1994, IEEE Trans. Signal Process..

[8] Yutaka Yamamoto,et al. Frequency responses for sampled-data systems-Their equivalence and relationships , 1994 .

[9] R.G. Shenoy. Analysis of multirate components and application to multirate filter design , 1994, Proceedings of ICASSP '94. IEEE International Conference on Acoustics, Speech and Signal Processing.

[10] Tongwen Chen,et al. Design of multirate filter banks by /spl Hscr//sub /spl infin// optimization , 1995 .