Signal processing using bilinear and nonlinear time-frequency-joint-representations

  • Harold Szu
C. Wigner Distributions
Part of the Lecture Notes in Physics book series (LNP, volume 278)


Bilinear and nonlinear signal processing are described based upon the following observations:
  1. (a)

    A phase space for signal processing is identified with a time-frequency joint representation (TFJR) that appears almost everywhere naturally, for example in bats, in music, etc.

  2. (b)

    A sudden slow-down mechanism is responsible for the transition from a phase coherent-to-incoherent wavefront and provides us the sharpest tone transduction from a Békésy traveling wave in a model of the inner ear. The cause of the slowdown is physically identified to be due to three forces. This has been used to derive a cubic deceleration polynomial responsible for a cusp bifurcation phenomenon which occurs for every tone transducted along the nonuniform elastic membrane. The liquid-filled inner ear cochlea channel is divided by the membrane into an upper duct that has hair cells for the forward sound-generated flow and the lower duct for the backward balance-return flow.

  3. (c)

    Both cross Wigner distribution (cross-WD) W21 (t0, v0) and cross Woodward ambiguity function (cross-AF) A21(τ,μ,) are bilinear TFJR's in the central (t0,v0) and difference (τ,μ) coordinates for two independent signals s1(t1) and s2(t2). A neurogram is a nonlinear TFJR.

  4. (d)

    Active probing uses (Doppler μ, delay τ)-weighted correlation, cross-AF, while passive listening uses (mean v0, central t0)- selected convolution, cross-WD. Both are useful for post processing in a marginal probability sense. A neurogram is useful for reverberation and noise robust detection pre-processing.


Such an algorithm of neurogram is exemplified by a chirp signal in noise and reverberation.


Wave Breaking Return Flow Basilar Membrane Wigner Distribution Ambiguity Function 


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Copyright information

© Springer-Verlag 1987

Authors and Affiliations

  • Harold Szu
    • 1
  1. 1.Naval Research LaboratoryWashington

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