H. Chen et al., BANDPASS PREFILTERING FOR EXPONENTIAL DATA FITTING WITH KNOWN FREQUENCY REGION OF INTEREST, Signal processing, 48(2), 1996, pp. 135-154
Prefiltering methods are presented for estimating the parameters of a
sum of exponentially damped sinusoids and applied for two purposes. Fi
rst, when all the sinusoids are of interest and the SNRs are low, a fi
lter 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 amplit
udes 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 Flu et al. (1993) for subspace and SVD-based estima
tion methods. In this paper, we present a more justifiable filter matr
ix that implements the FIR prefiltering as well as other filter matric
es for the IIR prefiltering. A theoretical analysis on a special case
of two exponentially damped sinusoids is given, which reveals the rela
tionship between the singular values/vectors of the prefiltered and or
iginal data matrices. The prefiltering technique can be used prior to
a subspace and SVD-based method. The benefits of the new filter matric
es used prior to the HTLS estimation method are confirmed through simu
lations.