A new optimal window [signal processing]

An optimal window that can provide the best tradeoff between the peak sidelobe level and the total sidelobe level is presented. Necessary and sufficient conditions are established for the optimal window. A design algorithm is presented, and examples are discussed. The examples demonstrate that the window is capable of much better performance than previously available windows, such as the Hamming window. Relationships between the maximum error and the mean-squared error are explored for the window optimization problem. It is concluded that the minimax and least squares approximations are both fundamentally inefficient. This conclusion is supported by experimental evidence and mathematical analyses. >

[1]  D. Yavuz,et al.  Some novel windows and a concise tutorial comparison of window families , 1978 .

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

[3]  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.

[4]  A. Willson,et al.  On the fast design of high-order FIR digital filters , 1985 .

[5]  L. Rabiner,et al.  A computer program for designing optimum FIR linear phase digital filters , 1973 .

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

[7]  R. Diderich.  Calculating Chebyshev shading coefficients via the discrete Fourier transform , 1974 .

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

[9]  Donald Goldfarb,et al.  A numerically stable dual method for solving strictly convex quadratic programs , 1983, Math. Program..

[10]  J. G. Ecker,et al.  A Dual Method for Quadratic Programs with Quadratic Constraints , 1975 .

[11]  D. Munson,et al.  A tomographic formulation of spotlight-mode synthetic aperture radar , 1983, Proceedings of the IEEE.

[12]  D. Slepian.  Prolate spheroidal wave functions, fourier analysis, and uncertainty — V: the discrete case , 1978, The Bell System Technical Journal.

[13]  John D. Mathews,et al.  The discrete prolate spheroidal filter as a digital signal processing tool , 1985, IEEE Trans. Acoust. Speech Signal Process..

[14]  D. Slepian,et al.  Prolate spheroidal wave functions, fourier analysis and uncertainty — II , 1961 .

[15]  Salvatore D. Morgera,et al.  The Levinson recurrence and fast algorithms for solving Toeplitz systems of linear equations , 1987, IEEE Trans. Acoust. Speech Signal Process..

[16]  A. H. Nuttal.  Generation of Dolph-Chebyshev weights via a fast Fourier transform , 1974 .