Multi-channel homomorphic wavelet estimation

Mark Christopher Lane
1983
Wavelet estimation can be posed as a multi-channel common information problem. Each channel of data is modeled as the convolution of a wavelet with an impulse sequence. A homomorphic transform maps the data from a convolutional to an additive space. The mapping may also effect partial separation of wavelet and impulses. In the additive space the wavelet can be estimated using averaging. This is termed cepstral averaging. This thesis reviews the homomorphic transform and provides a synthesis and
more » ... des a synthesis and comparison of the techniques available for its realization. The method of principal components for wavelet estimation is proposed as an alternative to cepstral averaging. The effect of noise on this method is investigated. The investigation shows that noise may cause principal components to produce estimates which are inferior to cepstral averaging. For these cases an alternate solution is proposed in which principal components are used in the original convolutional space. A wavelet is estimated by homomorphic separation for each data channel. Principal components may then be used to define a best estimate from this suite of estimates.
doi:10.14288/1.0052934 fatcat:7hloq4u2brek5g5tuu4gytrwgi