Adaptive SVD-based AR model order determination for time-frequency analysis of Doppler ultrasound signals

Abstract

The short-time Fourier transform provides a picture of the spectral components temporal location in time-varying signals, but its performance is limited by the intrinsic trade-off between time and frequency resolutions. In the present study, this problem is addressed using a spectral estimator based on a combination of the autoregressive (AR) modeling technique and a new automatic model order selection method. The order estimation is achieved by means of the singular value decomposition (SVD) of an appropriate data matrix in conjunction with a new criterion (dynamic mean evaluation, DME). The latter is used to decide which singular values correspond to the signal and which to the noise subspaces, avoiding an a priori threshold definition, thus giving the variable AR model order on consecutive short-time segments. Combination of the AR high frequency resolution capabilities and the SVD plus DME robustness and simplicity make the overall method reliable in many practical applications, mainly in the analysis of time-varying signals corrupted by noise. The proposed procedure has been applied to benchmark as well as to Doppler signal analysis. Some examples are reported confirming the above-mentioned properties.