Design of NPR DFT-Modulated Filter Banks via Iterative Updating Algorithm
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Design of NPR DFT-Modulated Filter Banks via Iterative Updating Algorithm Junzheng Jiang · Shan Ouyang · Fang Zhou
Received: 1 November 2011 / Revised: 19 October 2012 © Springer Science+Business Media New York 2012
Abstract In this paper, an efficient algorithm is proposed to design nearly-perfectreconstruction (NPR) DFT-modulated filter banks. First, the perfect-reconstruction (PR) condition of the oversampled DFT-modulated filter banks in the frequency domain is transformed into a set of quadratic equations with respect to the prototype filter (PF) in the time domain. Second, the design problem is formulated as an unconstrained optimization problem that involves PR condition and stopband energy of the PF. With the gradient vector of the objective function, an efficient iterative algorithm is presented to design the PF, which is updated with linear matrix equations at each iteration. The algorithm is identified as a modified Newton’s method, and its convergence is proved. Numerical examples and comparison with many other existing methods are included to demonstrate the effectiveness of the proposed method. Keywords DFT-modulated filter banks · Perfect reconstruction (PR) · Iterative updating program · Modified Newton’s method · Prototype filter
J. Jiang · S. Ouyang School of Information and Communication, Guilin University of Electronic Technology, Guilin 541004, P.R. China J. Jiang e-mail: [email protected] S. Ouyang e-mail: [email protected] F. Zhou () School of Life and Environmental Sciences, Guilin University of Electronic Technology, Guilin 541004, P.R. China e-mail: [email protected]
Circuits Syst Signal Process
1 Introduction Multirate filter banks have been thoroughly investigated and widely applied in digital signal processing [1–6, 8, 9, 11–15]. As a special class of multirate filter banks, modulated filter banks are popular, due to their easy design and fast implementation [1–4, 6, 9, 12–15]. Cosine-modulated filter banks (CMFBs) and DFT-modulated filter banks are two main types of modulated filter banks, and they have a close relation. Compared to CMFBs, DFT-modulated filter banks possess a unique merit to separate positive and negative frequency components into different subbands, a useful property in complex signal processing [7] and two-dimensional directional filter banks [8]. From applications, the nearly perfect reconstruction (NPR) DFT-modulated filter banks often achieve better performance than their PR counterparts [2, 3, 9, 13]. There are several methods to design NPR DFT-modulated filter banks. In [13], the NPR DFT-modulated filter banks are designed by the semi-definite program (SDP), and the designed prototype filters (PFs) are the global solutions of the optimization. However, the aliasing distortion of filter banks in [13] is controlled by the stopband characteristics of the PF. The reconstruction error of the obtained filter bank is restricted by the attainable stopband attenuation of the PFs. In [2], the bi-iterative quadratic program (BI-QP) algorithm is presented t
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