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Wigner Distribution Representation and Analysis of Audio Signals: An Illustrated Tutorial Review
The Wigner distribution provides a visual disply 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 instanteous frequency (from classical modulation theory). The energy spectrum (energy per frequency) and the 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 distibution are mathematically elegant and do merit in-depth study, a substantial amount of practical insignt, 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.
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