Time histories of longitudinal velocity fluctuations in the intermediate and far regions of the turbulent wake of a two-dimensional circular cylinder are analyzed by the wavelet transform employing the antisymmetric, Mexican-hat and Morlet wavelets. Contours of the wavelet transform in the (a, b) parameter space, where a is the scale and b is the temporal location of the center of the wavelet, are found to be basically similar for the three wavelets if the a-and b-axes are properly translated. This is particularly true for the Mexican-hat wavelet and the real part of the Morlet wavelet, both of which are symmetric with respect to the location b. The contours demonstrate the periodic velocity fluctuation associated with the Karman vortex street in the intermediate wake, the low-frequency modulation of the vortices in the vortex street, and the multi-scale structure in the far wake. The Morlet wavelet yields the most detailed multi-scale structure of the velocity fluctuations among the three wavelets.