Gabor wavelet function

The second exponential function in Eq. (29) is used in ordinary Fourier transforms, where no window is applied. In the Gabor wavelet transform a window around / = t is superposed by the first part of Eq. (29) (i.e., by the error function). On the other hand, in the classical Gabor transform, not the Gabor wavelet transform, a windowed Fourier transform with a fixed width window is applied, as illustrated in Fig. 39b. 

Figure 39 Examples of Gabor wavelet and Gabor function, (a) Gabor wavelet (dilated window) (b) Gabor function (fixed window width). (Sheng, 1996.) (With permission of CRC Press)...

The finest possible simultaneous encoding of position and frequency requires wavelets which minimize the product Ax A. Such functions are called Gabor wavelets and have... 

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