One Method For Design of Lowpass Narrowband Filters

This paper presents a lowpass narrowband filter design method with a small number of products per output sample (MPS). The method is based on the use of a sharpened Cascade Integrator-Comb (CIC) filter and an Interpolated Finite Impulse Response (IFIR) structure. INTRODUCTION In many communications and signal processing systems it is necessary to isolate a very narrow band signal from a very wide band signal. The use of a Finite Impulse Response (FIR) digital filter has the advantages of guaranteed stability, absence of limit cycles, and linear phase, if desired. The main disadvantage of FIR filters in narrowband filtering is that the large filter length is required. This implies a large number of arithmetic operations per output sample in the filter implementation. The number of multipliers per output sample (MPS) is equal to or half of the length of the filter in the nonlinear and linear phase cases, respectively. Several FIR design methods have been proposed to reduce the number of arithmetic operations. The interpolated FIR (IFIR) filter proposed by Y. Neuvo at al., 1984, is one of the computationally efficient realizations for narrowband FIR filters. The IFIR filter is a cascade of two filters ) ( ) ( ) ( z I z G z H M = , (1) where G(zM) is an expanded shaping or model filter, I(z) is an interpolator or images suppressor and M is the interpolator factor. The advantage of this structure is based on the design of a narrowband FIR prototype filter H(z) by using smaller order filters, G(z) and I(z). For more details of the IFIR structure see Y. Neuvo at al., 1984. The minimum number of MPS in an IFIR structure is computed for a chosen interpolator factor M such that the orders of the filters G(z) and I(z) are equal or close to each other. Hence, an increment in the interpolator factor means an exponential grow in the interpolation filter order. We can notice that fewer MPS would be needed if the interpolator filter is implemented with fewer products. This idea was used by D. Pang, at al., 1991, where a low order B-spline filter is used as the interpolator filter. In this paper we propose to use the sharpened Cascaded Integrator-Comb (CIC) filter as the interpolator in the IFIR structure for narrowband filtering. A CIC filter uses only one product per output sample. In this way the number of MPS is considerably reduced. The filter sharpening technique, proposed by J. F. Kaiser and R. W. Hamming, 1984, and generalized by R. J. Hartnett, and G. F. Boudreaux, 1995, is used to improve the frequency domain response of the CIC filter. The CIC filter characteristics are reviewed in section II. In section III the filter sharpening technique is described. The proposed method and an illustrative example are presented in section IV. CASCADED INTEGRATOR-COMB FILTER The Cascaded Integrator-Comb (CIC) structure was proposed by E. B. Hogenauer, 1981, as an efficient structure for multirate filtering. A CIC decimation filter consists of two sections • Cascade of L integrators operating at the high rate