A Recursive Method for the Approximation of LTI Systems Using Subband Processing

• Published in: IEEE transactions on signal processing Vol. 58; no. 3; pp. 1025 - 1034
• Main Authors: Marelli, D., Minyue Fu
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.03.2010; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithms; Allocations; Applied sciences; Approximation; Computational complexity; Computer simulation; Convolution; Delay; Detection, estimation, filtering, equalization, prediction; Exact sciences and technology; Filter bank; Finite impulse response filter; Information, signal and communications theory; Least squares method; Mathematical analysis; Mathematical models; Miscellaneous; Modeling; Optimization; Optimization methods; Robust stability; Signal and communications theory; Signal processing; Signal processing algorithms; Signal, noise; subband signal processing; system analysis and design; Telecommunications and information theory; Transfer functions; Transfer matrix; Subband decomposition; Logarithmic function; Fast Fourier transformation; system analysis and design; System design; Algorithm; Computational complexity; Modeling; Implementation; Optimization; subband signal processing; Weighting; Simulation; Optimal allocation; Least squares method; Recursive method; Signal processing; Filter bank; Transfer function; Pole zero method
• ISSN: 1053-587X; 1941-0476
• DOI: 10.1109/TSP.2009.2034933

Using the subband technique, an LTI system can be implemented by the composition of an analysis filterbank, followed by a transfer matrix (subband model) and a synthesis filterbank. The advantage of this approach is that it offers a good tradeoff between latency and computational complexity. In this paper we propose an optimization method for approximating an LTI system using the subband technique. The proposed method includes optimal allocation of parameters from different FIR entries of the subband model, while keeping constant the total number of parameters, for a better utilization of the available coefficients. The optimization is done in a weighted least-squares sense considering either linear or logarithmic amplitude scale. Simulation results demonstrate the advantages of the proposed method when compared with classical implementation approaches using pole-zero transfer functions or segmented FFT algorithms.