1.1. Steps in the initial auditory processing. 4 2 THE TIME-FREQUENCY ENERGY REPRESENTATION 2.1. Short-time spectrum of a steady-state Iii. 9 2.2. Smoothed short-time spectra. 9 2.3. Short-time spectra of linear chirps. 13 2.4. Short-time spectra of /w /'s. 15 2.5. Wide band spectrograms of /w /'s. 16 Spectrograms of rapid formant motion. 2.6. 17 2.7. Wigner distribution and spectrogram. 21 2.8. Wigner distribution and spectrogram of cos wot. 23 2.9. Concentration ellipses for transform kernels. 28 2.10. Concentration ellipses for complementary kernels. 42 42 2.11. Directional transforms for a linear chirp. 47 2.12. Spectrograms of /wioi/ with different window sizes. 2.13. Wigner distribution of /wioi/. 49 2.14. Time-frequency auorrelation function of /wioi/. 49 2.15. Gaussian transform of Iwioi/. 50 2.16. Directional transforms of lwioi/. 52 3 TIME-FREQUENCY FILTERING 3.1. Recovering the transfer function by filtering. 57 3.2. Estimating 'aliased' transfer function. 61 3.3. T-F auorrelation function of an impulse train. 70 3.4. T-F auorrelation function of LTI filter output. 70 Windowing recovers transfer function. 3.5. 72 3.6. Shearing the time-frequency auorrelation function. 75 3.7. T-F auorrelation function for FM filter. 76 3.8. T-F auorrelation function of FM filter output. 77 3.9. Windowing recovers transfer function. 79 4 THE SCHEMATIC SPECTROGRAM Problems with pole-fitting approach.