Frequency-Reponse Masking Techniques

Abstract

The initial concept of the frequency-response masking technique was introduced by Neuvo, Cheng-Yu and Mitra (1984). It was shown that the complexity of a linear phase FIR filter can be considerably reduced by using the cascade connection of an interpolated FIR (IFIR) filter and a properly designed FIR filter. The IFIR filter transfer function is obtained by replacing the unit delay z-1 with the delay block z-M, where M is an integer. In this way, the frequency response of the IFIR filter is made periodic. The FIR filter in the cascade is used to eliminate (mask) the images from the IFIR filter frequency response. Two years later, Lim (1986) proposed a complete approach for the application of frequency-response masking technique in designing narrow-band and arbitrary-band linear phase FIR filters. It was shown that the approach given in (Lim, 1986) results in a linear phase FIR filter with a small fraction of nonzero coefficients, and thus is suitable for implementing sharp filters with arbitrary bandwidths. The arithmetic complexity is considerably smaller in comparison with the arithmetic complexity of an optimal FIR filter having the equivalent frequency response. This approach is applied later to IIR filters by Johansson and Wanhammar (1997, 2000). The overall filter is composed of an IIR periodic model filter and its complementary periodic filter, and FIR linearphase masking filters. In this way, the arbitrary-band filter can be designed. For a narrowband filter, the cascade of a periodic filter and masking filter can be used. The frequency-response masking approach is suitable for digital filters with sharp transition bands. Compared to the classical single-filter design, this technique offers the advantage of lower coefficients’ sensitivity, higher computation speed and lower power consumption. Recently, the application of frequency-response masking approach has been extended to filter banks to achieve a sharp band-separation with reduced computational complexity (Furtado, Diniz, Netto, and Saramäki, T. 2005; Rosenbaum, Lövenborg, and Johansson, 2007). In this chapter, we review the frequency-response masking techniques for narrow-band and arbitrary bandwidth IIR filters. We demonstrate through examples that very selective characteristics can be obtained using relatively low-order sub-filters. In this way, stable, low-sensitive filters are obtained.