THE PHASE PROPERTY OF A FINITE REALIZATION OF RANDOM NOISE AND ITS INFLUENCE ON DECONVOLUTION *

A finite realization of a discrete random noise process may be considered as a one‐sided energy signal. Its phase property can then be described by means of the center position. The samples of such a realization are the components of a random signal vector and the center position is therefore a random variable. A statistical analysis shows that the expected value of the center position equals half the time duration of the realization. This implies that the Z‐transform of the realization may be expected to have an equal number of poles and zeros inside and outside the unit circle. The standard deviation from the expected value of the center position is shown to depend on the time duration of the realization and on the autocorrelation of the process. It follows that, for processes that can be described by the convolution of a white series and a disturbance wavelet, the center position is independent of the phase property of the wavelet. A conclusion based on these results is that the homomorphic technique of wavelet estimation through cepstrum stacking must give questionable outcomes. Another conclusion is that the super‐position of a realization of random noise on a minimum phase wavelet will in general give a mixed phase resulting signal. It is pointed out that schemes for the derivation of deconvolution filters do not take account of this phenomenon.