Different Approaches for the Design of IFIR Compaction Filter

Authors: Sheeba V.S, Elizabeth Elias

Abstract:

Optimization of filter banks based on the knowledge of input statistics has been of interest for a long time. Finite impulse response (FIR) Compaction filters are used in the design of optimal signal adapted orthonormal FIR filter banks. In this paper we discuss three different approaches for the design of interpolated finite impulse response (IFIR) compaction filters. In the first method, the magnitude squared response satisfies Nyquist constraint approximately. In the second and third methods Nyquist constraint is exactly satisfied. These methods yield FIR compaction filters whose response is comparable with that of the existing methods. At the same time, IFIR filters enjoy significant saving in the number of multipliers and can be implemented efficiently. Since eigenfilter approach is used here, the method is less complex. Design of IFIR filters in the least square sense is presented.

Keywords: Principal Component Filter Bank, InterpolatedFinite Impulse Response filter, Orthonormal Filter Bank, Eigen Filter.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1330483

References:

[1] P. P. Vaidyanathan, "Theory of optimal orthonormal subband coders" IEEE Trans. Signal processing,46(6):1528-1543, June 1998
[2] P. P. Vaidyanathan, Multirate systems and Filterbanks Pearson education. Inc.1993 Chapter 6
[3] R. A. Horn and C. R. Johnson, Matrix Analysis. Cambridge, U.K: Cambridge Univ. Press, 1985, pp 176-177, 192-193.
[4] Sony Akkarakkaran and P. P. Vaidyanathan, "Filter bank optimization with convex objectives and the optimality of principal component forms", IEEE Trans. SP. vol 49 no.1 pp 100-114, Jan 2001
[5] Ahmet Kirac and P. P. Vaidyanathan, "Theory and design of optimum FIR compaction filters," IEEE Trans. Signal Processing, vol. 46, no. 4, pp. 903-919, Apr. 1998
[6] J. Tuqan and P. P. Vaidynathan, "A state space approach to the design of globally optimal FIR energy compaction filters", IEEE Trans. Signal Processing, vol.48, no. 10, pp. 2822-2838, Oct. 2000
[7] Andre Thacenko and P. P. Vaidyanathan, " Iterative gradient technique for the design of least squares optimal FIR magnitude squared Nyquist filters", IEEE Int. Conf. On Acoust., Speech, and Signal Processing,May 2004.
[8] Yuan-Pei Lin and P. P. Vaidyanathan , "An iterative approach to the design of IFIR matched filters", International Symposium on Circuits and Systems, June 9-12, 1997,Hong Kong
[9] V.P.Sathe and P. P. Vaidyanathan , "Effects of Multirate systems on the statistical properties of random signals", IEEE Transaction on Signal processing, vol.41, No.1, January 1993, 131-146.
[10] P. P. Vaidyanathan and Sony Akkarakkaran, "A review of the theory and applications of optimal subband and transform coders", Applied and computational harmonic analysis, 10,254- 289(2001).
[11] T Q Nguyen, "The design of arbitrary FIR digital filters using the Eigenfilter method", IEEE Trans. Signal processing, 41(3):1128-1139, Mar 1993
[12] P. P. Vaidyanathan, T Q Nguyen, Zinnur Doganata, Tapio Saramaki, "Improved Technique for Design of Perfect Reconstruction FIR QMF Banks with Lossless Polyphase Matrices", IEEE trans. on ASSP,vol 37,no 7 1989
[13] P. P. Vaidyanathan, "Eigenfilters: A New Approach to Least-Squares FIR Filter Design and Applications Including Nyquist Filters", IEEE trans. on CAS, Vol 34, no.1,1987.