Frequency estimation using warped discrete Fourier transform
Signal Processing - Special section: Hans Wilhelm Schüßler celebrates his 75th birthday
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One of the main goals in ultrasonic Doppler blood flow measurement is the estimation of the mean velocity. The Doppler signal's instantaneous frequency has traditionally been used to estimate the mean velocity. In this work, a non-uniform discrete time frequency distribution is proposed: the warped discrete Wigner-Ville distribution (WTFDWV). The proposed procedure estimates the instantaneous frequency by concentrating the frequency resolution around the instantaneous frequency to adjust a parabola on the main spectral lobe. The parabola's maximum is then located over the instantaneous frequency. As a result, a better precision is obtained in the spectral estimation by using a WTFDWV for noisy signals when compared to other methods such as the Discrete Wigner-Ville Time Frequency Distribution (DTFDWV) with the instantaneous frequency calculated as the centroid of the spectrum. It is observed that the WTFDWV acts as a band-pass filter around the instantaneous frequency. Additionally, this paper proposes a generalisation of the WTFDWV as a Warped Discrete Time Frequency Distribution Class.