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Wigner Distribution Representation and Analysis of Audio Signals: An Illustrated Tutorial Review

The Wigner distribution provides a visual display of quantitative information about how a signal's energy is distributed in both time and frequency. Through its low-order moments the Wigner distribution embodies the fundamentally important concepts of both Fourier analysis and time-domain analysis. Signal energy is distributed in such a way that specific frequencies are localized in time by the group delay time (from classical filter theory) and at specific instants in time the frequency is given by the instantaneous frequency (from classical modulation theory). The energy spectrum (energy per frequency) and instantaneous power (energy per time) are specified by the zero-order moments of the distribution. The net positive volume of the Wigner distribution is numerically equal to the signal's total energy. While the theoretical underpinnings of the Wigner distribution are mathematically elegant and do merit in-depth study, a substantial amount of practical insight, understanding, and interpretive skill can be gained by carefully examining a wide variety of computed Wigner distributions such as those of the audio signals presented in this brief report.

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