With the additional constraint of requiring only two codeword lengths, lossless codes of blocks of size n generated by stationary memoryless binary sources are studied. For arbitrary /spl delta/>0, classical large-deviation inequalities imply the existence of codes attaining an expected redundancy of the order O(n/sup -1/2+/spl delta//). It is shown that it is not possible to construct lossless codes with two codeword lengths having rate of order better or equal to O(n/sup -1/2/).

Some properties of second-order random processes such as, stationarity and scaling, are characterized via corresponding (multiscale) properties of their discrete wavelet transform. The single scale characterizations valid in the continuous setting do not extend to the discrete setting. Some extensions of these results are also indicated.

Without finite moment conditions, some properties of random processes, such as stationarity and self-similarity, are characterized via corresponding properties of their wavelet transform. Anyone of these distributional properties of the wavelet transform characterizes the corresponding property of the increments of the random process, of order equal to the order of regularity of the analyzing wavelet. Extensions of these results to random fields are then indicated.

Some second-order properties of random processes such as periodic correlation, stationarity, harmonizability, self-similarity, are characterized via corresponding properties of their wavelet transform: any one of these properties of the wavelet transform characterizes the corresponding property of the increments of the random process, of order equal to the order of regularity of the analyzing wavelet. These results are then specialized to fractional Brownian motion and other self-similar processes.>

The estimation of power is problematic when the amplitudes in the discrete spectral component are random. An example of this is a mixed spectrum stationary Gaussian process with mean zero. In this regard, it is shown that the maximum likelihood estimator of the power from a random sample of peaks exceeding a relatively large threshold, the peak estimator is more efficient than the sample variance from a random sample of the same size of signal values. When evaluated from nonrandom samples, indications are that the peak estimator may still have a relatively small mean square error.