The paper deals with simultaneous noise suppression and signal compression in order to reconstruct and to monitor quasi harmonic signals. In particular one is interested in monitoring and recognizing signals as they occur in rail vehicle systems. One describes an algorithm to estimate discrete signals from their noisy observations using a library of nonorthonormal bases. The described technique combines the shrinkage technique and techniques in regression analysis using Shannon Entropy function and Cross Entropy function. When the problem is to compress and to detect the signals one needs an algorithm which can illuminate the difference between the noise and the desired signal. Recursive residual iterations with cosine and sine bases allow to reconstruct the signal and the noise
with the best discernable bases. Simulations using real measured data from an electrical railway line are included to illustrate and to analyse the effectiveness of the proposed method.