Real time composite signal decomposition

The recovery was investigated in real-time of an unknown wavelet from a composite signal in the presence of additive noise; the composite signal consists of a wavelet and its echoes. Two techniques, the power and complex cepstra, were used in the wavelet recovery procedure. An alternate definition of the power cepstrum is presented which closely relates the two techniques, and makes computation of the power cepstrum from the complex cepstrum trivial. This unification led to the discovery of a third cepstrum technique, the phase cepstrum, which like the power cepstrum is useful in the determination of echo epoch times. Several problems inherent in cepstrum computation were examined. These problems include linear phase terms, phase unwrapping errors, aliasing, and oversampling. The effects of windowing (as used to reduce leakage in spectral analysis) at various stages in the wavelet recovery system are discussed. Algorithms suitable for use in a real-time wavelet recovery system were examined.