Adaptive signal processing
Generating functionology
A Method of Inverse Filter Design Based on Cepstrum Measure
AINA '05 Proceedings of the 19th International Conference on Advanced Information Networking and Applications - Volume 2
Digital Signal Processing
Adaptive minimum symbol-error rate equalization for quadrature-amplitude modulation
IEEE Transactions on Signal Processing
IEEE Transactions on Information Theory
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Inverse-system approximation using finite-impulse responses (FIR) is essential to a broad area of signal-processing applications. The conventional Wiener filtering techniques based on the least-square approach cannot provide an analytical framework simultaneously governing two crucial problems, namely, the selection of model order and the evaluation of asymptotical error bounds. In fact, the square approximation error induced from the FIR realization of a linear time-invariant system is quite complicated, specifically for those system transfer functions possessing repeated zeros with large multiplicities. Therefore, in this paper, we establish an isomorphism to characterize the z-transform pairs. In this mathematical paradigm, we will elaborate the problem of approximating an inverse system or filter with an infinite number of coefficients by an FIR filter and derive the new L1 and L2 approximation-error bounds between the actual inverse filter and the corresponding approximated FIR. Our new theories, analysis, and bounds can be utilized to quantify the appropriate model order for the inverse-system approximation that is often needed for signal processing, control, communications, etc.