GaborWavelet
represents a Gabor wavelet of frequency 6.
GaborWavelet[w]
represents a Gabor wavelet of frequency w.
Details
- GaborWavelet defines a family of complex non-orthogonal wavelets.
- The wavelet function (
) is given by 
. - GaborWavelet can be used with such functions as ContinuousWaveletTransform and WaveletPsi, etc.
Examples
open allclose allScope (2)
GaborWavelet is used to perform ContinuousWaveletTransform:
Use WaveletScalogram to get a time scale representation of wavelet coefficients:
Use InverseWaveletTransform to reconstruct the signal:
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:
Properties & Relations (4)
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:
Text
Wolfram Research (2010), GaborWavelet, Wolfram Language function, https://reference.wolfram.com/language/ref/GaborWavelet.html.
CMS
Wolfram Language. 2010. "GaborWavelet." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/GaborWavelet.html.
APA
Wolfram Language. (2010). GaborWavelet. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/GaborWavelet.html