Spectral Analysis in Frequency and Time Domain for Noisy Time Series

In this paper the orthogonal decomposition is used in order to reconstruct the noiseless component of a temporal stochastic process. For weakly stationary processes, the proposed methodology is based on the joint application of the spectral analysis in the frequency domain (Fourier analysis) and in the time domain (Karhunen Lo´eve expansion). For non stationary processes the orthogonal decomposition is realized in the wavelet domain.