### Abstract

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.

Original language | English |
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Pages (from-to) | 207-209 |

Number of pages | 3 |

Journal | IEEE Signal Processing Letters |

Volume | 4 |

Issue number | 7 |

DOIs | |

Publication status | Published - Jul 1997 |

### Keywords

- acoustic correlation
- acoustic receivers
- acoustic signal processing
- acoustic wave scattering
- deconvolution
- receivers
- wavelet transforms
- acoustic scatterer
- acoustic signals
- continuous wavelet transform
- deconvolution equation
- density function
- orthogonal projection
- received signal
- subspace
- transmitted signal
- wideband correlation receiver output
- wideband deconvolution
- wideband density function
- wideband processing

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## Cite this

Rebollo-Neira, L., & Fernandez-Rubio, J. (1997). On wideband deconvolution using wavelet transforms.

*IEEE Signal Processing Letters*,*4*(7), 207-209. https://doi.org/10.1109/97.596889