Time-frequency analysis: theory and applications
Time-frequency analysis: theory and applications
Discrete-time signal processing (2nd ed.)
Discrete-time signal processing (2nd ed.)
IEEE Transactions on Signal Processing
Design of higher order polynomial Wigner-Ville distributions
IEEE Transactions on Signal Processing
Time--frequency feature representation using energy concentration: An overview of recent advances
Digital Signal Processing
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The peak of the polynomial Wigner-Ville distribution (PWVD) can be used for estimating the instantaneous frequency (IF) of monocomponent polynomial phase signals. However, the PWVD kernel, optimized to yield a time-frequency distribution (TFD) localized along the IF, comprises of fractional-time-sampled signals. When implemented in a discrete-time scenario, this calls for signal interpolation. We study three interpolation schemes--linear, cubic polynomial and sinc and derive expressions for the variance of the interpolated samples in the presence of noise. In representing nonstationary signals using the PWVD, the instantaneous energy content of noise auto-terms and signal-noise cross-terms is found to be the least for linear interpolation scheme. For polynomial IF estimation using the peak of the PWVD, it was found that linear interpolation is a computationally efficient way of obtaining reasonably good estimates at low signal-to-noise ratios (SNRs). For high SNRs, sinc interpolation outperforms the other two schemes. Similar results were found when the experiment was extended to sinusoidal IF signals also.