Signal processing using bilinear and nonlinear time-frequency-joint-representations
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.
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.
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.
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.
KeywordsWave Breaking Return Flow Basilar Membrane Wigner Distribution Ambiguity Function
Unable to display preview. Download preview PDF.
- 4.H.H. Szu and J.A. Blodgett, “Wigner Distribution and Ambiguity Function,” In: “Optics in Four Dimensions-1980,” edited by M.A. Machado and L.M. Narducci, Pub. by Am. Inst. Phys. Conf. Proc. 65, No. 1, pp. 355-381, 1981.Google Scholar
- 5.H.H. Szu and J.A. Blodgett, “Image Processing for Acoustical Patterns,” In: “Workshop on Image Processing for Ocean Acoustics,” May 6–8, 1981, Woods Hole, Mass.Google Scholar
- 6.H.H. Szu, “Optical Data Processing Using Wigner Distribution,” In: “Symposium on 2-D Signal Processing Techniques and Applications,” March 3–5, 1981, Washington, D.C. (NRL Memo Report 4526, DTIC No. 1180069).Google Scholar
- 12.M.J. Bastiaans, “Wigner distribution functions and their applications to first order Optics,” Opt. Comm. 32, 3238, Jan. 1980.Google Scholar
- 16.T.A.C.M. Claasen and W.F.G. Mecklenbrauker, “The Wigner distribution-a tool for time-frequency signal analysis, Part I: continuous-time signals,” Philips J. Res., Vol. 35, pp. 217–250, 1980. “Part II: discrete signals,” Philips J. Res., Vol. 35, pp. 276–300, 1980. “Part III: relations with other time-frequency signal transformations,” Philips J. Res., Vol. 35, pp. 372–389, 1980.MathSciNetMATHGoogle Scholar
- 19.C.P. Janse and A.J.M. Kaizer, “The Wigner Distribution: A Valuable Tool for Investigating Transient Distortion,” J. Audio Eng. Soc. Vol. 32, No. 11, 868–882, Nov. 1984.Google Scholar
- 22.N. Weidenhof and J.M. Waalwijk, “Wigner Distributions: A Refined Mathematical Tool for Appraising Loudspeakers,” Funk-Tech. (GERMANY), Vol. 39, No. 9, 371–373, Sept. 1984.Google Scholar
- 24.G. Neuweiler, In: “Animal Sonar Systems,” R.G. Busnel and J.F. Fish, editors, Plenum, New York 1980.Google Scholar
- 26.D.R. Griffin, “Listening in the Dark,” Yale, New Haven 1958.Google Scholar
- 28.A.J. Hudspeth, “The Hair Cells of the Inner Ear,” Scient. Amer., pp. 54–64, Jan. 1983.Google Scholar
- 32.G. Neuweiler, “How bats detect flying insects,” Physics Today, pp. 34–40, Aug. 1980.Google Scholar
- 33.R. Thom, “Stabilitd Structurelle et Morphogenése,” (New York, Benjamin, 1972).Google Scholar
- 34.H.H. Szu, “Applications of Wigner and Ambiguity Functions to Optics,” Proc. IEEE Int. Symp. Circuits and Systems, San Jose, CA, May 5–7, 1986.Google Scholar
- 35.G. Von Békésy, “Experiments in Hearing,” New York McGraw Hill, 1960.Google Scholar
- 40.S. Shamma, “Speech Processing in the Auditory System I: The representation of speech sounds in the response of the auditory nerve, vol. 78 (5), pp. 1612–1622, NOV. 1985; II ibid. pp. 1622-1632.Google Scholar
- 43.H. Szu, “Nonlinear Signal Computing Using Neurograms,” to appear in a book: “Optical and Hybrid Computing,” (Edited by H. Szu, Oct. 1986, published by SPIE).Google Scholar