WINDOW BASED PROTOTYPE FILTER DESIGN FOR HIGHLY OVERSAMPLED FILTER BANKS IN AUDIO APPLICATIONS David Hermann, Edward Chau AMI Semiconductor Waterloo, Ontario, Canada Robert D. Dony, Shawki M. Areibi School of Engineering University of Guelph Guelph, Ontario, Canada ABSTRACT This paper describes a window based method for designing near perfect-reconstruction prototype filters for highly oversampled, com- plex modulated filter banks. The design method extends some well- known simple methods for critically sampled filter banks to the over- sampled case and to the case of different length analysis and synthe- sis filters. This design method is simple and effective for designing a large range of filter bank configurations. The design method is par- ticularly useful in developing audio applications using oversampled filter banks where the target system’s requirements are highly vari- able. The simplicity and flexibility of the design method means that this one method can be used to generate multiple prototype filters as the application requirements change. Index Terms— FIR digital filters, channel bank filters, hearing aids, audio systems 1. INTRODUCTION Oversampled filter banks have found use in a variety of applications in recent years. In particular, they have found commercial applica- tions in low-power audio signal processing for devices such as hear- ing aids [1]. Other researchers have also highlighted their potential in audio processing for applications such as acoustic echo cance- lation, dynamic range compression and noise reduction. For audio processing devices such as hearing aids, highly oversampled filter banks offer a compromise between aliasing reduction in each sub- band and achieving ultra low delay through the filter bank, e.g. less than 10 ms with 16 kHz sampling. Solutions for designing perfect-reconstruction (PR) oversampled filter banks have been presented in the literature [2]. However, the PR condition is routinely violated in audio processing applications. The nature of subband audio processing including subband gain ap- plication and subband adaptive filters means that each subband sig- nal is modified between analysis and synthesis such that the PR condition no longer holds. Thus, it is of interest to explore near perfect-reconstruction (NPR) oversampled filter banks. Relaxing the PR condition allows the filter bank designer more flexibility in their application. In the context of audio applications, the amount of dis- tortion allowable in the NPR filter bank will vary with the specific audio processing system. For high-fidelity systems, a dynamic range of 90 dB or significantly above is desirable. For systems that have a higher noise floor due to issues such as microphone noise, a range of only 60 dB may be acceptable. These diverse requirements further emphasize the need for a flexible design strategy that can accommo- date a wide variety of filter bank configurations. This paper presents a simplified method for designing prototype x(n) h 0 (n) R X 0 (m) R g 0 (n) h 1 (n) R X 1 (m) R g 1 (n) h k (n) R X k (m) R g k (n) . . . + h N-1 (n) R X N-1 (m) R g N-1 (n) y(n) . . . . . . . . . . . . . . . Fig. 1. Block Diagram of an Oversampled Filter Bank filters for a highly oversampled NPR filter bank using window-based FIR filter designs. This approach will extend similar approaches used in conventional critically sampled NPR filter banks. The goal of this design method is to develop a simple and flexible method that can be applied for a wide variety of oversampled filter bank config- urations. The rest of this paper is organized as follows. First, we review the formulation of an oversampled filter bank including the equations which will be useful in the design method to be presented. Second, we provide a brief summary of other methods in the literature and identify how this new method is different. Finally, we present the new design method and analyze its performance under varying de- sign parameters. 2. OVERSAMPLED FILTER BANKS This section will briefly review the basic structure of complex mod- ulated oversampled filter banks in order to set a framework for the prototype filter design problem. A block diagram view of an over- sampled filter bank is shown in Figure 1. The input signal, x(n), is filtered by N channel filters denoted h k (n) for k =0, 1,...,N - 1. The resulting filtered channel signals are downsampled by a factor of R to create the oversampled subband channel signals X k (m), where m is a subband time index. The oversampling ratio is then defined as OS = N/R, and for highly oversampled filter banks we will consider OS ≥ 2. The synthesis portion of the filter bank involves upsampling the subband signals by the decimation factor, R, filter- ing with the synthesis filters (denoted g k (n)) and then summation of the filtered signals. As usual for these systems, we define the analysis and synthe- Copyright 2006 IEEE. Published in the IEEE 2007 International Conference on Acoustics, Speech, and Signal Processing (ICASSP 2007), scheduled for April 16-20, 2007 in Honolulu, Hawaii. Personal use of this material is permitted. However, permission to reprint/ republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works, must be obtained from the IEEE. Contact: Manager, Copyrights and Permissions / IEEE Service Center / 445 Hoes Lane / P.O. Box 1331 / Piscataway, NJ 08855-1331, USA. Telephone: + Intl. 908-562-3966.