A discussion on the expression proposed by Weiss et al. (see J. Acoust. Soc. Amer., vol.96, p.850-6 and p.857-66, 1994 and IEEE Signal Processing Mag., vol.11, p.13-32, 1994) for deconvolving the wideband density function is presented. We prove here that such an expression reduces to be proportional to the wideband correlation receiver output, or continuous wavelet transform of the received signal with respect to the transmitted one. Moreover, we show that the same result has been implicitly ass...
A discussion on the expression proposed by Weiss et al. (see J. Acoust. Soc. Amer., vol.96, p.850-6 and p.857-66, 1994 and IEEE Signal Processing Mag., vol.11, p.13-32, 1994) for deconvolving the wideband density function is presented. We prove here that such an expression reduces to be proportional to the wideband correlation receiver output, or continuous wavelet transform of the received signal with respect to the transmitted one. Moreover, we show that the same result has been implicitly assumed by Weiss et al., when the deconvolution equation is derived. We stress the fact that the analyzed approach is just the orthogonal projection of the density function onto the image of the wavelet transform with respect to the transmitted signal. Consequently, the approach can be considered a good representation of the density function only under the prior knowledge that the density function belongs to such a subspace. The choice of the transmitted signal is thus crucial to this approach.
A discussion on the expression proposed in [1]–[3]
for deconvolving the wideband density function is presented. We
prove here that such an expression reduces to be proportional
to the wideband correlation receiver output, or continuous wavelet
transform of the received signal with respect to the transmitted
one. Moreover, we show that the same result has been implicitly
assumed in [1], when the deconvolution equation is derived. We
stress the fact that the analyzed approach is just the orthogonal
projection of the density function onto the image of the wavelet
transform with respect to the transmitted signal. Consequently,
the approach can be considered a good representation of the
density function only under the prior knowledge that the density
function belongs to such a subspace. The choice of the transmitted
signal is thus crucial to this approach.
Citation
Rebollo Neira, L.; Fernández Rubio, J. A. On wideband deconvolution using wavelet transform. IEEE Signal Processing Letters, 1997, vol. 4, núm. 7, p. 207-209.