GaborWavelet

GaborWavelet is used to perform ContinuousWaveletTransform:

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:

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: