Partial Fraction Signal Decomposition and Time-Frequency Representation

Abstract

Summary We present a new method for obtaining the time-frequency decomposition of a non-stationary signal. The input signal is modeled as a dynamic short-time autoregressive process. From the analytic signal or complex trace, we compute the AR coefficients or prediction error operator (PEO), in sliding time windows. The inverse of the Z-transform of the PEOs can be represented by a sum of partial fractions, each one related to a single pole. Each pole may be used to deflate the PEO, allowing us to rewrite the AR representation of the signal as a sum of signal components. Also, the position of each pole provides the dominant frequency, which is useful to distribute the signal component in the time-frequency domain. The signal components are obtained by convolving the input signal with the reduced PEOs, scaled by the partial fractions coefficients. The new time-frequency signal decomposition method is demonstrated on synthetic data.