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A new approach to representing a time-limited, and essentially bandpass signal x(t) , by a set of discrete frequency values is proposed. The set of discrete frequency values is the set of locations along the frequency axis at which (real and/or imaginary parts of) the Fourier transform of the signal x(t) cross certain levels (especially zero level). Analogously, invoking time-frequency duality, a set of time instants denoting the zero/level crossings of a waveform x(t) can be used to represent a bandlimited spectrum X(f) . The proposed signal representation is based on a simple bandpass signal model that exploits our prior knowledge of the bandwidth/timewidth of the signal. We call it a Sum-of-Sincs (SOS) model, where Sinc stands for the familiar sinx/x function. Given the discrete fequency/time locations, we can accurately reconstruct the signal x(t) or the spectrum X(f) by solving a simple eigenvalue or a least squares problem. Using this approach as the basis, we propose an analysis/synthesis algorithm to decompose and represent complex multicomponent signals like speech over the entire time-frequency region. The proposed signal representation is an alternative to standard analog to discrete conversion based on the sampling theorem, and in principle, possesses some of the desirable attributes of signal representation in natural sensory systems.
Audio, Speech, and Language Processing, IEEE Transactions on (Volume:18 , Issue: 1 )
Date of Publication: Jan. 2010