A wavelet is finite energy and band-pass,
it oscillates in time like a short wave, hence the name "Wavelet". The
wavelet has an average value of zero
The wavelet transform convolves the
signal x(t) with a wavelet family which is the translation and dilation
of a unique wavelet
where t and s are the translation
and dilation parameters of the wavelet transform.
The wavelet works
like a band-pass filter and the wavelet coefficient can
be viewed as a filtering of the signal x(t) by the filter, as shown belown.
Learning Program(Not aviable here, this is a part of the
web course "Wavelet Tutorial" ) show how to extract the different frequency
components by dilation of the mother wavelet.