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→Scale factor: Fixed inconsistency (changed "scale factor" to "\sigma parameter") and added context (interpolation between time-series and Fourier transform). |
m →Continuous wavelet transform properties: Replaced time-like \sigma convention with frequency-like parameter, to better match convention used in Morlet wavelet. |
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==Continuous wavelet transform properties==
In definition, the continuous wavelet transform is a [[convolution]] of the input data sequence with a set of functions generated by the mother wavelet. The convolution can be computed by using a [[fast Fourier transform]] (FFT) algorithm. Normally, the output <math>X_w(a,b)</math> is a real valued function except when the mother wavelet is complex. A complex mother wavelet will convert the continuous wavelet transform to a complex valued function. The power spectrum of the continuous wavelet transform can be represented by <math>|X_w(a,b)|^2</math> .
[[File:Wavelet scale sweep for FM signal.gif|thumb|300px|Visualizing the effect of changing a [[Morlet wavelet|Morlet wavelet's]] <math>\sigma</math> parameter, which
==Applications of the wavelet transform==
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