A new approach to representing a time-limited, and essentially bandlimited signal x(t), by a set of discrete frequency/time values is proposed. The set of discrete frequencies is the set of frequency locations at which (real and imaginary parts of) the Fourier transform of x(t) cross certain levels and the set of discrete time values corresponds to the traditional level crossings of x(t). The proposed representation is based on a simple bandpass signal model called a Sum-of-Sincs (SOS) model, that exploits our knowledge of the bandwidth/timewidth of x(t). Given the discrete fequency/time locations, we can reconstruct the x(t) by solving a least-squares problem. Using this approach, we propose an analysis/synthesis algorithm to decompose and represent composite signals like speech.
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