Design of Digital Filter Banks for Speech Analysis

Many speech processing systems are based on the concept of shorttime spectrum analysis. 1,2 Spectrum analyzers for such systems often consist of a set of bandpass filters whose combined passbands cover a desired frequency range. Although continuous-time filters have traditionally been used in filter banks for speech analysis, hardware realizations of digital filters are now available, 3 and the advantages which digital filters offer should be exploited in filter bank design. These advantages include: flexibility of design of the individual bandpass filters, precision of realization, stability of digital hardware, and the efficiency of realization of the filter bank afforded by the possibility of multiplexing the digital hardware. Thus it is important to consider design techniques for filter banks composed of digital bandpass filters. To focus on the basic concepts in filter bank design, it is useful to define an ideal filter bank spectrum analyzer. Figure 1 depicts such a filter bank composed of digital filters whose impulse responses are denoted by hk(nT), k = 0, 1, ··· , M, where /T is the sampling frequency of the input signal.* Such a filter bank constitutes an ideal spectrum analyzer if the input x(nT) (with possibly further band limiting) can be synthesized exactly (within some fixed delay) by a linear * The filter ha(nT) is a lowpass filter which is included for completeness although this band is usually not analyzed in practical speech analysis systems. 3097