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The real cepstrum is derived from the magnitude spectrum of a time series. You cannot reconstruct the original time series from the real cepstrum because the real cepstrum does not preserve the phase information of the original time series.
The real cepstrum is useful for feature extraction from homomorphic time series, such as the following applications:
Use the TSA Real Cepstrum VI to compute the real cepstrum of a time series. As with power spectrum estimation, you can estimate the real cepstrum using the fast Fourier transform (FFT) or the AR model of the time series.