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 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag 1987

Authors and Affiliations

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

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