This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.

# GaborWavelet

 GaborWavelet represents a Gabor wavelet of frequency 6. GaborWavelet[w]represents a Gabor wavelet of frequency w.
• GaborWavelet defines a family of complex non-orthogonal wavelets.
• The wavelet function () is given by .
Wavelet function:
Wavelet function:
 Out[2]=
 Out[4]=
 Scope   (2)
Use WaveletScalogram to get a time scale representation of wavelet coefficients:
Use InverseWaveletTransform to reconstruct the signal:
Wavelet function as a function of frequency w:
 Applications   (1)
Resolve a cosine wave with frequency 10 Hz:
Perform a continuous wavelet transform on the data:
Frequencies resolved by the transform are the inverse of the scales:
Plot WaveletScalogram to verify that the 10 Hz frequency is resolved by the seventh octave:
GaborWavelet with a certain frequency is similar to MorletWavelet:
Wavelet function and its Fourier transform:
GaborWavelet does not have a scaling function:
The central frequency of the GaborWavelet[w] is approximately w:
Compute the wavelet function with frequency parameter :
Plot the real part of a wavelet function overlaid by a sinusoid at the central frequency:
Imaginary part:
New in 8