WAVELET TRANSFORM
A wavelet is a waveform of
effectively limited duration that has an average value of zero. Wavelets are
also defined as mathematical functions that cut up data into different
frequency components and then study each component with a resolution matched to
its scale. The comparison of wavelets with sine waves, which are the basis of
Fourier analysis, Sinusoids do not have limited duration
they extend from minus to plus infinity. Where sinusoids are smooth and
predictable, wavelets tend to be irregular and asymmetric. Fourier analysis
consists of breaking up a signal into sine waves of various frequencies.
Similarly, wavelet analysis is the breaking up of a signal into shifted and
scaled versions of the original (or mother) wavelet. It also makes sense that local features can be described
better with wavelets that have local extent.
Wavelet Transform is used to split
the signal into a bunch of signals and represents the same signal, but all
corresponding to different frequency bands. The principle advantage is they
provide what frequency bands exists at what time intervals. Wavelet transform
of any function f at frequency a & time b is computed by correlating f with
wavelet atom .
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