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.