Translations:Zero-phase wavelets/1/en

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The autocorrelation function is symmetric and two-sided with a central positive maximum. Except in the case of periodicity, the Autocorrelation will damp out symmetrically in both directions from this central maximum. Moreover, it will damp out with a certain speed. If we perform a Fourier analysis on an autocorrelation, we will find the following: The autocorrelation curve can be represented as a sum of cosine curves of different frequencies and different amplitudes. At the central point of the autocorrelation, all of those cosine curves will be in phase - that is, the crest of each cosine wave will occur at the maximum (or central) value of the autocorrelation. No negative cosine curves (i.e., those that are out of phase) occur, nor do any sine curves occur. Thus, there are no phase differences; the phase is zero for every frequency. As a result, any autocorrelation function is a zero-phase waveform. A zero-phase wavelet is always two-sided.