Theoretical analysis on the finite-support approximation for the mixing-phase FIR systems. (English) Zbl 1169.94309
Summary: The inverse system approximation using the finite impulse responses (FIR) and the corresponding model-order determination are essential to a broad area of science and technology utilizing signal processing. To the best of our knowledge, there exists no explicit formulation of the exact \(L_{2}\) approximation error for the truncated inverse filters. The approach to determine the minimum inverse model-order subject to the maximum allowable \(L_{2}\) approximation error is also in demand. In this paper, we present two \(L_{2}\) approximation error measures and the two corresponding optimal finite-support approximates. Also, we derive the explicit \(L_{2}\) approximation error functions with respect to roots, multiplicities and model orders for these two kinds of approximates. Then, we propose a new algorithm to determine the minimum total model order of the appropriate truncated inverse filter to achieve a specified \(L_{2}\) approximation error. Our newly derived \(L_{2}\) approximation error evaluation method can be employed for signal processing, telecommunication, control systems involving the inverse filtering in the future. Besides, our novel model-order determination algorithm can be utilized for efficient dynamic memory allocation in a wide variety of applications since such a minimum total model order is proportional to the memory usage for any inverse filter implementation.
MSC:
| 94A12 | Signal theory (characterization, reconstruction, filtering, etc.) |
Keywords:
inverse system; FIR realization; approximation error; optimal finite-support approximates; equalizationReferences:
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