Showing papers on "Quadrature mirror filter published in 1972"

Adaptive Decomposition of a Composite Signal of Identical Unknown Wavelets in Noise

Abstract: An algorithm is discussed which decomposes a noisy composite signal of identical but unknown multiple wavelets overlapping in time. The decomposition determines the number of wavelets present, their epochs, amplitudes, and an estimate of the basic wavelet shape. The algorithm is an adaptive decomposition filter which is a combination tion of three separate filters. One is an adaptive cross-correlation filter which resolves the composite signal from noise by an iteration procedure; this is followed by a wavelet extraction filter which ferrets out the basic wavelet form, and last there appears an inverse filter which achieves decomposition of the composite signal in the time domain. The decomposition algorithm can be applied to echoes and overlapping wavelets which might arise in radar, sonar, seismology, or electro-physiology. The proposed theory has been thoroughly simulated and selected experimental results are presented to demonstrate the technique. These include decomposition of brain waves evoked by visual stimulation.

Computer-designed Wiener Filters For Seismic Data

Abstract: This paper is concerned with differences in the frequency content of signal and noise on seismic traces. In order to develop a filter which has applicability over some considerable spatial range, special consideration is given to basic differences in the shape and the frequency content of individual signal and noise wavelets (events) on these traces. Therefore, a so-called “wavelet” Wiener filter is introduced which suppresses “noise” wavelets and enhances “signal” wavelets; this filter can be contrasted with an ordinary Wiener filter which discriminates between signal and noise on the additional basis of the statistics of the repetition of wavelets along the seismic trace. A technique for the automatic derivation of (wavelet) Wiener filters for seismic data by a digital computer is developed. The filters are time dependent to the extent that independent filters are derived at a sequence of data windows which are specified by the operator; criteria for selecting the window positions are given. The overall technique for the computer derivation of Wiener filters is demonstrated with synthetic and actual seismic data. A discussion of the wavelet Wiener filter and its relation to the ordinary Wiener filter is appended to this paper with a discussion of the effects of finite data windows on the eduction of the wavelet Wiener filter.