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Windowed Fourier transform of two-dimensional quaternionic signals. (English) Zbl 1196.42009
The authors generalize the classical windowed Fourier transform to quaternion-valued 2-dimensional signals. Using the spectral representation of the quaternionic Fourier transform, they derive some properties such as reconstruction formula, reproducing kernel, isometry, orthogonality relation, and uncertainty principle. Using the Gaussian window, quaternionic Gabor filters are obtained. Some examples are given, too.
MSC:
42B10Fourier type transforms, several variables
30G30Other generalizations of analytic functions (one variable)
References:
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