Hindawi Publishing Corporation ISRN Signal Processing Volume 2013, Article ID 148646, 8 pages http://dx.doi.org/10.1155/2013/148646 Research Article Studies on Z-Window Based FIR Filters Rahul Pachauri, 1 Rajiv Saxena, 1 and Sanjeev N. Sharma 2 1 Department of Electronics & Communication Engineering, Jaypee University of Engineering & Technology, Guna 473226, India 2 Department of Electronics & Communication Engineering, Samrat Ashok Technological Institute, Vidisha 464001, India Correspondence should be addressed to Rahul Pachauri; pachauri.123@gmail.com Received 7 June 2013; Accepted 29 July 2013 Academic Editors: I. Guler and C. S. Lin Copyright © 2013 Rahul Pachauri et al. his is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. As per classiication of the window functions, the Z-windows are grouped in the category of steerable side-lobe dip (SSLD) windows. In this work, the application of these windows for the design of FIR ilters with improved ilter parameters has been explored. he numbers of dips with their respective positions in the side-lobe region have been compositely used to tailor the window shape. Filter design relationships have been established and included in this paper. Simultaneously, an application of these Z-window based FIR ilters in designing two-channel quadrature mirror ilter (QMF) bank has been presented. Better values of reconstruction and aliasing errors have been achieved in contrast to the Kaiser window based QMF bank. 1. Introduction he inite impulse response (FIR) ilters are one of the pro- minent building blocks used in various applications of digital signal processing. hese ilters have got more popularity than ininite impulse response (IIR) ilters because of their inherent stability and linear phase characteristics [1]. he straightforward approach to design the FIR ilters is trun- cating the ideal impulse response using windows. Careful selection of window function reduces the ripples introduced by truncation in the frequency response of these ilters [2]. In the literature, several categories of windows have been proposed [3, 4]. One of the important categories of windows is steerable side lobe dips (SSLD) windows in which deep dips can be steered in the side lobes. Tseng windows and Zhong windows (ZWs) are the examples of SSLD windows [5, 6]. he ZW proposed by Zhong et al. [6] has simple expressions in either of the domains, good overall spectral characteristics, SSLD property and easy and lexible design technique as compared to Tseng window. hese features of ZW motivated us to study this window from the FIR ilter design perspective. Prior to this work, the design of FIR ilters using ZW has also been reported by Sharma et al. [7] in which ilter order () and transition bandwidth (TBW) have been minimized at the cost of higher passband ripple (PBR) and stopband attenuation (SBA). he ilters designed by Sharma et al. [7] are having SBA in the range of 18–42 dB with single dip steered at an appropriate location in the side lobes of ZW. Followed by this work, the ZW ilter (ZWF) has been designed using the traditional window based approach by Pachauri et al. [8] in which the PBR and SBA has been minimized at the cost of higher ilter order. he expression of the ilter order was modiied in [8] and was made directly proportional to the number of SSLDs introduced in the ZW. It has also been demonstrated in [8] that the half main lobe width (HMLW) of ZW varies with dip displacement up to a certain position and ater that it becomes constant. If the dips are introduced below this threshold position then the ilter order reduces and PBR and SBA increase [7], whereas the ilter order increases and PBR and SBA decrease when the dips are inserted on the other side of the threshold position [8]. With this background on spectral response of ZW, the studies available in [7, 8], low pass ilters have been designed using Z-window in this work. Performance of these ilters has been studied by varying number of dips in ZW along with respective variation in their position. his study helped us in establishing an application of this ilter in multirate signal processing. he remaining part of this paper has been organized as follows. In the next section ZW has been introduced and its properties from the ilter design perspective have been dis- cussed. In Section 3, an algorithm to establish the empirical design relationships for ZWF has been developed. Simulation results and the performance analysis of the proposed ilters are included in Section 4. Design of quadrature mirror ilter