Designed to follow an introductory text on psychoacoustics, this book takes readers through the mathematics of signal processing from its beginnings in the Fourier transform to advanced topics in modulation, dispersion relations, minimum phase systems, sampled data, and nonlinear distortion. While organised like an introductory engineering text on signals, the examples and exercises come from research on the perception of sound. A unique feature of this book is its consistent application of the Fourier transform, which unifies topics as diverse as cochlear filtering and digital recording. More than 250 exercises are included, many of them devoted to practical research in perception, while others explore surprising auditory illusions generated by special signals. Periodic signals, aperiodic signals, and noise -- along with their linear and nonlinear transformations -- are covered in detail. More advanced mathematical topics are treated in the appendices. A working knowledge of elementary calculus is the only prerequisite. Indispensable for researchers and advanced students in the psychology of auditory perception.
Preface.- 1. Pure Tones.- 2. Complex Representation.- 3. Power, Intensity, and Decibels.- 4. Intensity and Loudness.- 5. Fourier Series.- 6. Perception of Periodic Complex Tones.- 7. Delta Functions.- 8. Fourier Integral.- 9. Filters.- 10. Auditory Filters.- 11. Musical Measures of Frequency.- 12. Pitch of Sine Tones.- 13. Applications of the Fourier Transform.- 14. Correlation Functions and Spectra.- 15. Delay-and-Add Filtering.- 16. Probability Density Functions.- 17. Beats and Amplitude Modulation.- 18. The Envelope.- 19. Frequency Modulation.- 20. Modulation Detection and Perception.- 21. Sampled Signals.- 22. Nonlinear Distortion.- 23. Noise.- 24. Signal Detection Theory.- Appendices A - K.- References.- Index.
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...of great importance to the hearing science community... If I were to give an al³+