# GaborWavelet

represents a Gabor wavelet of frequency 6.

GaborWavelet[w]

represents a Gabor wavelet of frequency w.

# Examples

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## Basic Examples(1)

Wavelet function:

## Scope(2)

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:

## 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:

Imaginary part:

Wolfram Research (2010), GaborWavelet, Wolfram Language function, https://reference.wolfram.com/language/ref/GaborWavelet.html.

#### 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

#### BibTeX

@misc{reference.wolfram_2023_gaborwavelet, author="Wolfram Research", title="{GaborWavelet}", year="2010", howpublished="\url{https://reference.wolfram.com/language/ref/GaborWavelet.html}", note=[Accessed: 24-February-2024 ]}

#### BibLaTeX

@online{reference.wolfram_2023_gaborwavelet, organization={Wolfram Research}, title={GaborWavelet}, year={2010}, url={https://reference.wolfram.com/language/ref/GaborWavelet.html}, note=[Accessed: 24-February-2024 ]}