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In this talk, we give a rigorous description of the mathematical foundations underlying discrete-time audio signal processing. We explore how a time-frequency representation called the short-time Fourier transform (STFT) can be used to analyze and modify signal content. We then describe various ways of isolating (possibly modified) signal components and resynthesizing them from the STFT. Since the STFT is only optimal for analyzing signal components with constant or near-constant frequency, we propose a modification of the STFT called the chirped quilted STFT (CQSTFT) that leads to better performance for signals with time-varying oscillatory components. The idea of CQSTFT is to "demodulate" signal components so that they can be analyzed like constant-frequency components, and to conduct this demodulation in an automatic, signal-adaptive manner. We demonstrate how CQSTFT-based techniques can be used to extract vocal signatures from recordings of female Bornean gibbon great calls for the purpose of distinguishing individuals in the population (speaker classification). Finally, we use the CQSTFT to analyze vocal clips from the famous motion picture "The Room."

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