... Figure 10: Mean power spectrum obtained by time-averagi ng the energy map at each duration. For non-periodic signals, the mean wavelet spectrum is similar to the Fourier spectrum. ... The compromise we reached in allowing for single bump localization (something Fourier cannot do) reduces the spectral accuracy. ... Denote by the Fourier transform of the signal, the Fourier transform of the Mexican hat wavelet. ... by which the wavelet transform is a band-pass filtered Fourier Transform. ...