Recursive Nth-band digital filters- Part I: Design and properties

We investigate the properties of a special class of recursive polyphase filters whose subfilters are distinct allpass filters. On the basis of the discovered properties, a Remez-type algorithm is constructed for designing these filters. The proposed algorithm is faster and gives higher filter selectivities than other existing methods. Better understanding of the filter properties allows us to select the branch filter orders such that the filter complexity is minimized. In addition to nonlinear-phase filters, the algorithm is applicable to the design of approximately linear-phase filters. Several examples are included illustrating the efficiency of the proposed design scheme. The characteristics of the resulting filters are exposed by means of experimental results, and the implementation of the allpass branch filters is discussed. In a companion paper [33], we use these polyphase filters as basic building blocks in constructing efficient filters for sampling rate alteration. In addition, it is shown how the don't care bands, which cannot be avoided in filters of this type, can be suppressed by using an additional correction filter stage.

[1]  J. Rice.  The approximation of functions , 1964 .

[2]  Gabor C. Temes,et al.  Computer-aided network optimization the state-of-the-art , 1967 .

[3]  Leland B. Jackson,et al.  On the interaction of roundoff noise and dynamic range in digital filters , 1970, Bell Syst. Tech. J..

[4]  J. Craig,et al.  Digital filters for sample-rate reduction , 1972 .

[5]  L. Rabiner,et al.  A digital signal processing approach to interpolation , 1973 .

[6]  S. Mitra,et al.  Digital all-pass networks , 1974 .

[7]  Jacques Lucien Daguet,et al.  Interpolation, extrapolation, and reduction of computation speed in digital filters , 1974 .

[8]  L. Rabiner,et al.  Optimum FIR Digital Filter Implementations for Decimation, Interpolation, and Narrow-Band Filtering , 1975 .

[9]  L. Rabiner,et al.  A novel implementation for narrow-band FIR digital filters , 1975 .

[10]  R. Shively.  On multistage finite impulse response (FIR)filters with decimation , 1975 .

[11]  Georges Bonnerot,et al.  Digital filtering by polyphase network:Application to sample-rate alteration and filter banks , 1976 .

[12]  L. Rabiner,et al.  Further considerations in the design of decimators and interpolators , 1976 .

[13]  W. Wegener.  Wave digital directional filters with reduced number of multipliers and adders , 1979 .

[14]  T. Parks,et al.  A class of infinite-duration impulse response digital filters for sampling rate reduction , 1979 .

[15]  Lars Taxén,et al.  Polyphase filter banks using wave digital filters , 1981 .

[16]  Tamás Henk,et al.  The generation of arbitrary-phase polynomials by recurrence formulae , 1981 .

[17]  F. Mintzer,et al.  On half-band, third-band, and Nth-band FIR filters and their design , 1982 .

[18]  Tor A. Ramstad.  Digital Two-Rate IIR and Hybrid IIR/FIR Filters for Sampling Rate Conversion , 1982, IEEE Trans. Commun..

[19]  C. Sidney Burrus,et al.  Optimum FIR and IIR multistage multirate filter design , 1983 .

[20]  Reinaldo A. Valenzuela,et al.  Digital signal processing schemes for efficient interpolation and decimation , 1983 .

[21]  Rashid Ansari,et al.  Efficient sampling rate alteration using recursive (IIR) digital filters , 1983 .

[22]  T. Saramaki,et al.  A class of linear-phase FIR filters for decimation, interpolation, and narrow-band filtering , 1984 .

[23]  C. Sidney Burrus,et al.  Multirate filter designs using comb filters , 1984 .

[24]  Lajos Gazsi,et al.  Explicit formulas for lattice wave digital filters , 1985 .

[25]  Sanjit K. Mitra,et al.  A new class of uniform filter banks based on recursive Nth-band filters , 1986, ICASSP '86. IEEE International Conference on Acoustics, Speech, and Signal Processing.

[26]  L. Gazsi,et al.  A new design method for polyphase filters using all-pass sections , 1986 .

[27]  Markku Renfors,et al.  Recursive Nth-band digital filters- Part II: Design of multistage decimators and interpolators , 1987 .