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Morlet wavelet
In mathematics, the Morlet wavelet (or Gabor wavelet)〔(A Real-Time Gabor Primal Sketch for Visual Attention ) "The Gabor kernel satisfies the admissibility condition for wavelets, thus being suited for multi-resolution analysis. Apart from a scale factor, it is also known as the Morlet Wavelet."〕 is a wavelet composed of a complex exponential (carrier) multiplied by a Gaussian window (envelope). This wavelet is closely related to human perception, both hearing〔 and vision.〔J. G. Daugman. Uncertainty relation for resolution in space, spatial frequency, and orientation optimized by two-dimensional visual cortical filters. ''Journal of the Optical Society of America A'', 2(7):1160–1169, July 1985.〕
==History==
In 1946, physicist Dennis Gabor, applying ideas from quantum physics, introduced the use of Gaussian-windowed sinusoids for time-frequency decomposition, which he referred to as ''atoms'', and which provide the best trade-off between spatial and frequency resolution.〔 These are used in the Gabor transform, a type of short-time Fourier transform.〔(Time-Frequency Dictionaries ), Mallat〕 In 1984, Jean Morlet introduced Gabor's work to the seismology community and, with Goupillaud and Grossmann, modified it to keep the same wavelet shape over equal octave intervals, resulting in the first formalization of the continuous wavelet transform.〔http://rocksolidimages.com/pdf/gabor.pdf〕 (See also Wavelet history)
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