In a general sense this paper represents an effort to clarify the relationship of discrete and continuous wavelet transforms. More narrowly, it focuses on bringing together two separately motivated implementations of the wavelet transform, the algorithme U trous and Mallat's multiresolution decomposition. It is observed that these algorithms are both special cases of a single filter bank structure, the discrete wavelet transform, the behavior of which is governed by one's choice of filters. In fact, the h trow algorithm, originally devised as a computationally efficient implementation, is more properly viewed as a nonorthonormal multiresolution algorithm for which the discrete wavelet transform is exact. Moreover, it is shown that the commonly used Lagrange i~ trous filters are in one-to-one correspondence with the convolutional squares of the Daubechies filters for orthonormal wavelets of compact support. A systematic framework for the discrete wavelet transform is provided, and conditions are derived under which it computes the continuous wavelet transform exactly. Suitable filter constraints for finite energy and boundedness of the discrete transform are also derived. Finally, relevant signal processing parameters are examined, and it is remarked that orthonormality is balanced by restrictions on resolution.

Adaptive linear interference suppression for directsequence (DS) code-division multiple access (CDMA) is studied in the presence of time-and frequency-selective fading. Interference suppression is achieved with an adaptive digital filter which spans a single symbol interval. Both decision-directed and blind adaptive algorithms, which do not require a training sequence, are considered. Modifications to least squares adaptive algorithms are presented which are compatible with differential coding and detection. For frequency-selective fading, adaptive algorithms are presented based upon different assumptions concerning knowledge of the desired user's channel. Specifically, the cases considered are as follows: 1) perfect knowledge of the desired channel; 2) knowledge of only the relative path delays; and 3) knowledge of only one delay corresponding to the strongest path. Computer simulation results are presented which compare the performance of these algorithms with the analogous RAKE receivers. These results show that for case 3), even slow fading can cause a significant degradation in performance. Effective use of channel parameters in the adaptive algorithm reduces the sensitivity to fade rate, although moderate to fast fading can significantly compromise the associated performance gain relative to the RAKE receiver.

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