Time Windows for Linear Prediction of Speech

This report examines the time windows used for linear prediction (LP) analysis of speech. The goal of windowing is to create frames of data each of which will be used to calculate an autocorrelation sequence. Several factors enter into the choice of window. The time and spectral properties of Hamming and Hann windows are examined. We also consider windows based on Discrete Prolate Spherical Sequences including multiwindow analysis. Multiwindow analysis biases the estimation of the correlation more than single window analysis. Windows with frequency responses based on the ultraspherical polynomials are discussed. This family of windows includes Dolph-Chebyshev and Saramaki windows. This report also considers asymmetrical windows as used in modern speech coders. The frequency response of these windows is poor relative to conventional windows. Finally, the presence of a “pedestal” in the time window (as in the case of a Hamming window) is shown to be deleterious to the time evolution of the LP parameters. Time Windows for Linear Prediction of Speech 1 TimeWindows for Linear Prediction of Speech

[1]  Louis L. Scharf,et al.  Multiwindow estimators of correlation , 1998, IEEE Trans. Signal Process..

[2]  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.

[3]  Kurt S. Riedel,et al.  Minimum bias multiple taper spectral estimation , 2018, IEEE Trans. Signal Process..

[4]  Peter Kabal.  Windows for Transform Processing , 2005 .

[5]  R. Schafer,et al.  On the use of the I 0 -sinh window for spectrum analysis , 1980 .

[6]  H. Rohling,et al.  Discrete time window functions with arbitrarily low sidelobe level , 1983 .

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

[8]  A. Walden,et al.  Spectral analysis for physical applications : multitaper and conventional univariate techniques , 1996 .

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

[10]  G. J. V. D. Maas,et al.  A Simplified Calculation for Dolph‐Tchebycheff Arrays , 1953 .

[11]  Norman C. Beaulieu,et al.  Parametric construction of Nyquist-I pulses , 2004, IEEE Transactions on Communications.

[12]  Thomas T. Taylor,et al.  Dolph Arrays of Many Elements , 1953 .

[13]  Peter Kabal.  Ill-conditioning and bandwidth expansion in linear prediction of speech , 2003, 2003 IEEE International Conference on Acoustics, Speech, and Signal Processing, 2003. Proceedings. (ICASSP '03)..

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

[15]  K. Al-Naimi,et al.  Improved LSF estimation through anti-aliasing filtering , 2002, Speech Coding, 2002, IEEE Workshop Proceedings..

[16]  Harry L. Van Trees,et al.  Optimum Array Processing: Part IV of Detection, Estimation, and Modulation Theory , 2002 .

[17]  Louis L. Scharf,et al.  Lag-windowing and multiple-data-windowing are roughly equivalent for smooth spectrum estimation , 1999, IEEE Trans. Signal Process..

[18]  Hossein Najafzadeh-Azghandi,et al.  Perceptual Coding of Narrowband Audio Signals , 2001 .

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

[20]  L. Fox,et al.  Chebyshev polynomials in numerical analysis , 1970 .

[21]  Jes A. F. Florencio.  Investigating the use of asymmetric windows in CELP vocoders , 1993, 1993 IEEE International Conference on Acoustics, Speech, and Signal Processing.

[22]  Peter Kabal,et al.  The computation of line spectral frequencies using Chebyshev polynomials , 1986, IEEE Trans. Acoust. Speech Signal Process..

[23]  Wai C. Chu.  Gradient-descent based window optimization for linear prediction analysis , 2003, 2003 IEEE International Conference on Acoustics, Speech, and Signal Processing, 2003. Proceedings. (ICASSP '03)..

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