An efficient Haar wavelet-based approach for the harmonic retrieval problem

Modern subspace-based algorithms can offer high-resolution spectral estimates but with a cost of high computational complexity for the eigenvalue decomposition (EVD) involved. We propose a novel preprocessing scheme which can be used in conjunction with the subspace-based algorithms to alleviate the high computations previously required. The new scheme is to demodulate the input data first, and then takes the computationally efficient discrete-time Haar wavelet transform (HWT). Only the principle subband component (PSC) of the transformed data is kept for further processing, which not only retains the same amount of information but also possesses the same characteristic as that of the original (noiseless) harmonic data. The subspace-based algorithms are thus applicable to this new set of transformed data but with substantially reduced computational load. Some simulation results are provided to justify the proposed approach