### Abstract

Original language | English |
---|---|

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 |

### Fingerprint

### 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

### Cite this

*IEEE Signal Processing Letters*,

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

}

*IEEE Signal Processing Letters*, vol. 4, no. 7, pp. 207-209. https://doi.org/10.1109/97.596889

**On wideband deconvolution using wavelet transforms.** / Rebollo-Neira, L.; Fernandez-Rubio, J.

Research output: Contribution to journal › Article

TY - JOUR

T1 - On wideband deconvolution using wavelet transforms

AU - Rebollo-Neira, L.

AU - Fernandez-Rubio, J.

PY - 1997/7

Y1 - 1997/7

N2 - 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.

AB - 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.

KW - acoustic correlation

KW - acoustic receivers

KW - acoustic signal processing

KW - acoustic wave scattering

KW - deconvolution

KW - receivers

KW - wavelet transforms

KW - acoustic scatterer

KW - acoustic signals

KW - continuous wavelet transform

KW - deconvolution equation

KW - density function

KW - orthogonal projection

KW - received signal

KW - subspace

KW - transmitted signal

KW - wideband correlation receiver output

KW - wideband deconvolution

KW - wideband density function

KW - wideband processing

UR - http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=596889

U2 - 10.1109/97.596889

DO - 10.1109/97.596889

M3 - Article

VL - 4

SP - 207

EP - 209

JO - IEEE Signal Processing Letters

JF - IEEE Signal Processing Letters

SN - 1070-9908

IS - 7

ER -