Encoding Bandpass Signals Using Level Crossings: A Model-Based Approach

A new approach to representing a time-limited, and essentially bandlimited signal x(t), by a set of discrete frequency/time values is proposed. The set of discrete frequencies is the set of frequency locations at which (real and imaginary parts of) the Fourier transform of x(t) cross certain levels and the set of discrete time values corresponds to the traditional level crossings of x(t). The proposed representation is based on a simple bandpass signal model called a Sum-of-Sincs (SOS) model, that exploits our knowledge of the bandwidth/timewidth of x(t). Given the discrete fequency/time locations, we can reconstruct the x(t) by solving a least-squares problem. Using this approach, we propose an analysis/synthesis algorithm to decompose and represent composite signals like speech.

[1]  D. Slepian,et al.  On bandwidth , 1976, Proceedings of the IEEE.

[2]  Yehoshua Y. Zeevi,et al.  Image representation by zero and sine-wave crossings , 1987 .

[3]  B. Delgutte,et al.  Neural correlates of the pitch of complex tones. II. Pitch shift, pitch ambiguity, phase invariance, pitch circularity, rate pitch, and the dominance region for pitch. , 1996, Journal of neurophysiology.

[4]  Ray Meddis,et al.  Virtual pitch and phase sensitivity of a computer model of the auditory periphery , 1991 .

[5]  A. Oppenheim,et al.  Signal synthesis and reconstruction from partial Fourier-domain information , 1983 .

[6]  S. Seneff.  A joint synchrony/mean-rate model of auditory speech processing , 1990 .

[7]  E. Owens,et al.  An Introduction to the Psychology of Hearing , 1997 .

[8]  A. J. Jerri.  Correction to "The Shannon sampling theorem—Its various extensions and applications: A tutorial review" , 1979 .

[9]  Jae S. Lim,et al.  Signal reconstruction from Fourier transform sign information , 1985, IEEE Trans. Acoust. Speech Signal Process..

[10]  Oded Ghitza.  Auditory models and human performance in tasks related to speech coding and speech recognition , 1994 .

[11]  A uniqueness characterization in terms of signed magnitude for functions in the polydisc algebra A(Un) , 1989 .

[12]  Shlomo Shamai,et al.  On the duality of time and frequency domain signal reconstruction from partial information , 1985, IEEE Trans. Acoust. Speech Signal Process..

[13]  H. Voelcker,et al.  Clipping and Signal Determinism: Two Algorithms Requiring Validation , 1973, IEEE Trans. Commun..

[14]  Norman E. Hurt,et al.  Phase Retrieval and Zero Crossings , 1989 .

[15]  A. Requicha,et al.  The zeros of entire functions: Theory and engineering applications , 1980, Proceedings of the IEEE.

[16]  Jont B. Allen,et al.  Short term spectral analysis, synthesis, and modification by discrete Fourier transform , 1977 .

[17]  B. Logan.  Information in the zero crossings of bandpass signals , 1977, The Bell System Technical Journal.

[18]  M. Alexander,et al.  Principles of Neural Science , 1981 .

[19]  M. Hayes.  The reconstruction of a multidimensional sequence from the phase or magnitude of its Fourier transform , 1982 .

[20]  Rhee Man Kil,et al.  Auditory processing of speech signals for robust speech recognition in real-world noisy environments , 1999, IEEE Trans. Speech Audio Process..

[21]  A. Oppenheim,et al.  Signal reconstruction from phase or magnitude , 1980 .

[22]  Audra E. Kosh,et al.  Linear Algebra and its Applications , 1992 .

[23]  R.N. Bracewell,et al.  Signal analysis , 1978, Proceedings of the IEEE.

[24]  F. Itakura.  Line spectrum representation of linear predictor coefficients of speech signals , 1975 .

[25]  B. Delgutte,et al.  Neural correlates of the pitch of complex tones. I. Pitch and pitch salience. , 1996, Journal of neurophysiology.

[26]  Israel Bar-David,et al.  An Implicit Sampling Theorem for Bounded Bandlimited Functions , 1974, Inf. Control..