Least squared error FIR filter design with transition bands

The authors propose the use of transition bands and transition functions in the ideal amplitude frequency response to allow the analytical design of optimal least-squared-error FIR digital filters with an explicit control of the transition band edges. Design formulas are derived for approximations to ideal frequency responses which use pth-order spline transition functions. A mixed analytical and numerical method for zero-error weight in the transition bands and passband and stopband error weighting functions with an integral squared error approximation are derived. A variable-order spline transition function is developed, and a method for choosing the optimal order to minimize the integral squared approximation error is given. >

[1]  Walter Gautschi,et al.  Attenuation factors in practical Fourier analysis , 1971 .

[2]  D. Tufts,et al.  Designing simple, effective digital filters , 1970 .

[3]  Minsoo Suk,et al.  On the frequency weighted least-square design of finite duration filters , 1975 .

[4]  Thomas W. Parks,et al.  New results in the design of digital interpolators" ieee trans , 1975 .

[5]  D. Tufts,et al.  Designing digital low-pass filters--Comparison of some methods and criteria , 1970 .

[6]  D. Farden,et al.  Statistical design of nonrecursive digital filters , 1974 .

[7]  Carl de Boor,et al.  A Practical Guide to Splines , 1978, Applied Mathematical Sciences.

[8]  Charles Tzu-Tai Kao.  THE SPLINE APPROXIMATION IN SYSTEM SIMULATION BY DIGITAL COMPUTER , 1972 .

[9]  C. Lanczos.  Applied Analysis , 1961 .

[10]  H. W. Schüssler,et al.  A Hybrid system for the reconstruction of a smooth function from its samples , 1984 .

[11]  Truong Q. Nguyen,et al.  Eigenfilters: A new approach to least-squares FIR filter design and applications including Nyquist filters , 1987 .

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

[13]  Paul E. Fleischer.  Digital realization of complex transfer functions , 1965 .

[14]  T. W. Parks,et al.  Efficient solution of a Toeplitz-plus-Hankel coefficient matrix system of equations , 1980 .

[15]  John A. Pearce,et al.  A new window and comparison to standard windows , 1989, IEEE Trans. Acoust. Speech Signal Process..

[16]  Lawrence R. Rabiner,et al.  On the transition width of finite impulse-response digital filters , 1973 .

[17]  Joseph F. A. Ormsby,et al.  Design of Numerical Filters with Applications to Missile Data Processing , 1961, JACM.

[18]  D. C. Champeney.  A handbook of Fourier theorems , 1987 .

[19]  C. K. Yuen,et al.  Digital Filters , 1979, IEEE Transactions on Systems, Man, and Cybernetics.

[20]  P. M. Prenter.  Splines and variational methods , 1975 .

[21]  Hans-Wilhelm Schüßler.  Digitale Systeme zur Signalverarbeitung , 1973 .

[22]  G. Stoyan.  de Boor, C., A Practical Guide to Splines. Applied Mathematical Sciences 27. Berlin‐Heidelberg‐New York, Springer‐Verlag 1978. XXIV, 392 S., DM 32,50. US $ 17.90 , 1980 .

[23]  L. Jackson.  Digital filters and signal processing , 1985 .