The number of coefficients of the adaptive detection filters used in CDMA receivers is usually larger than the processing gain used in the system. Thus, when the value of this gain is high the adaptive filters suffer from slow convergence and high computational complexity. A similar problem occurs with the estimation/signal detection in UWB systems. The large number of channel paths common in such systems causes the quantities to be estimated to have a large number of elements, which requires, with conventional techniques, the processing of sets with large number of samples, thus resulting in a significant increase in the total computational cost of the receiver. This work focuses on a reduced-rank technique that is implemented through two phases, interpolation and decimation, in which given the decimation pattern chosen, the coefficients of the interpolator filter are optimized independently of the detection filter. Two algorithms are developed for the design of the interpolator filter. The first one is based on the maximization of the desired signal to noise ratio at the output of the reduced rank stage and the second considers the maximization of the desired signal to noise-plus-interference ratio at the output of the reduced rank stage. In general, the proposed reduced rank methods reduce the size of the observation vector according to the value set to the so called decimation factor. This reduction can have a significant impact on the complexity of equalization/detection algorithms that, for instance, have a quadratic increase of the computational cost with the size of the observation vector, as the RLS receivers implemented in the considered applications.