# Translations:Zero-phase wavelets/1/en

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 ${\displaystyle 180^{\circ }}$ 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.