A
wavelet is a
wave-like
oscillation with an
amplitude that begins at zero, increases, and then decreases back to zero. It can typically be visualized as a "brief oscillation" like one might see recorded by a
seismograph or
heart monitor. Generally, wavelets are purposefully crafted to have specific properties that make them useful for
signal processing. Wavelets can be combined, using a "reverse, shift, multiply and integrate" technique called
convolution, with portions of a known signal to extract information from the unknown signal. For example, a wavelet could be created to have a frequency of
Middle C and a short duration of roughly a
32nd note. If this wavelet was to be convolved with a signal created from the recording of a song, then the resulting signal would be useful for determining when the Middle C note was being played in the song. Mathematically, the wavelet will correlate with the signal if the unknown signal contains information of similar frequency. This concept of
correlation is at the core of many practical applications of wavelet theory.