Design of Nonrecursive Digital Filters Using the Ultraspherical Window Function

An efficient method for the design of nonrecursive digital filters using the ultraspherical window function is proposed. Economies in computation are achieved in two ways. First, through an efficient formulation of the window coefficients, the amount of computation required is reduced to a small fraction of that required by standard methods. Second, the filter length and the independent window parameters that would be required to achieve prescribed specifications in lowpass, highpass, bandpass, and bandstop filters as well as in digital differentiators and Hilbert transformers are efficiently determined through empirical formulas. Experimental results demonstrate that in many cases the ultraspherical window yields a lower-order filter relative to designs obtained using windows like the Kaiser, Dolph-Chebyshev, and Saramäki windows. Alternatively, for a fixed filter length, the ultraspherical window yields reduced passband ripple and increased stopband attenuation relative to those produced when using the alternative windows.

[1]  A. G. Deczky.  Unispherical windows , 2001, ISCAS 2001. The 2001 IEEE International Symposium on Circuits and Systems (Cat. No.01CH37196).

[2]  J. McClellan,et al.  A unified approach to the design of optimum FIR linear-phase digital filters , 1973 .

[3]  Anantha Chandrakasan,et al.  Approximate Signal Processing , 1997, J. VLSI Signal Process..

[4]  C.L. Dolph,et al.  A Current Distribution for Broadside Arrays Which Optimizes the Relationship between Beam Width and Side-Lobe Level , 1946, Proceedings of the IRE.

[5]  F. Harris.  On the use of windows for harmonic analysis with the discrete Fourier transform , 1978, Proceedings of the IEEE.

[6]  D. Shpak,et al.  A generalized Remez method for the design of FIR digital filters , 1990 .

[7]  J. McClellan,et al.  Chebyshev Approximation for Nonrecursive Digital Filters with Linear Phase , 1972 .

[8]  Andreas Antoniou,et al.  Generation of ultraspherical window functions , 2002, 2002 11th European Signal Processing Conference.

[9]  David R. Kincaid,et al.  Numerical mathematics and computing , 1980 .

[10]  Anantha P. Chandrakasan,et al.  Low-power digital filtering using approximate processing , 1996 .

[11]  A. Nuttall.  Some windows with very good sidelobe behavior , 1981 .

[12]  Jennifer Adams,et al.  FIR digital filters with least-squares stopbands subject to peak-gain constraints , 1991 .

[13]  L. Rabiner,et al.  Some comparisons between fir and iir digital filters , 1974 .

[14]  A. Antoniou.  Digital Signal Processing: Signals, Systems, and Filters , 2005 .

[15]  Andreas Antoniou,et al.  Design of Ultraspherical Window Functions with Prescribed Spectral Characteristics , 2004, EURASIP J. Adv. Signal Process..

[16]  O. Herrmann,et al.  Practical design rules for optimum finite impulse response low-pass digital filters , 1973 .

[17]  C.J. Pau,et al.  A stereo audio chip using approximate processing for decimation and interpolation filters , 2000, IEEE Journal of Solid-State Circuits.

[18]  T. Saramaki.  A class of window functions with nearly minimum sidelobe energy for designing FIR filters , 1989, IEEE International Symposium on Circuits and Systems,.

[19]  P. N. Paraskevopoulos,et al.  Modern Control Engineering , 2001 .

[20]  R. Streit.  A two-parameter family of weights for nonrecursive digital filters and antennas , 1984 .

[21]  Jrg Kaiser,et al.  Nonrecursive digital filter design using the I-sinh window function , 1977 .

[22]  J. Johnson,et al.  Low-Pass Filters Using Ultraspherical Polynomials , 1966 .

[23]  Milton Abramowitz,et al.  Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables , 1964 .