Bandpass prefiltering for exponential data fitting with known frequency region of interest

Abstract

Prefiltering methods are presented for estimating the parameters of a sum of exponentially damped sinusoids and applied for two purposes. First, when all the sinusoids are of interest and the SNRs are low, a filter can be designed to encompass all the sinusoids and to reduce the noise outside the passband. Secondly, when only some of the sinusoids are of interest with known frequencies but unknown dampings and amplitudes as typically occurs in NMR spectroscopy, a filter can be designed to encompass only the wanted peaks and suppress the unwanted ones and the noise. A prefiltering technique using a special filter matrix has been presented by Hu et al. (1993) for subspace and SVD-based estimation methods. In this paper, we present a more justifiable filter matrix that implements the FIR prefiltering as well as other filter matrices for the IIR prefiltering. A theoretical analysis on a special case of two exponentially damped sinusoids is given, which reveals the relationship between the singular values/vectors of the prefiltered and original data matrices. The prefiltering technique can be used prior to a subspace and SVD-based method. The benefits of the new filter matrices used prior to the HTLS estimation method are confirmed through simulations.