# Translations:Zero-phase wavelets/4/en

Within such a band, what sort of wavelet will have the smallest spread? We want to retain the sharpness of the spike as much as possible, so we will retain the cosine waves in this range of frequencies. Because all of the retained cosine waves are still in phase with their crests at time zero, the resulting wavelet will be symmetric and zero phase. Because all of the retained cosine waves will have the same amplitude, the amplitude spectrum will be level (flat) and will cover the entire available frequency range. The resulting wavelet will have the smallest value of the variance for the given frequency band. It will have a sharp central peak. It will oscillate, however, and such secondary oscillations (side lobes) are undesirable. We can reduce these secondary oscillations (side lobes) at the expense of increasing the width of the central peak. The result will be a zero-phase wavelet whose amplitude spectrum no longer will be absolutely flat in the available frequency range but still will be smooth and broad.