Spectral estimation based on subband decomposition by harmonic wavelet transform and modified group delay

Abstract

A new spectral estimator that exploits the simplicity and computational efficiency of the harmonic wavelet transform (HWT) for signal decomposition and the variance reduction property of the modified group delay (MGD), without any loss in frequency resolution, has been proposed. As the HWT directly provides the decimated subband components in the frequency domain, it enables direct application of the MGD to subband signals. In the HWT, the decomposition separates different parts of the spectrum into subbands and the decimation stretches each subband spectrum, hence the frequency resolution improves. Further as this also separates a low level spectral peak from a strong neighboring one, the signal detectability also improves. The MGD improves noise immunity, as it not only removes the spectral ripples due to leakage effect but also due to the associated noise. In view of these, the new estimator facilitates a significant improvement in: the reduction of variance, frequency resolution and signal detectability; compared with those of the MGD processing of fullband signals.