Usually, wavelet transform is real, so the output of a real sine is still a real sine. While that in STFT, the transform is complex, so the spectrogram is corresponding to the square of amplitude. For example, s(t) = A sin(xt), the intensity of frequency x at certain time instant in spectrogram is A^2, while that associated with scalogram is proportional to [A sin(xt)]^2. The other difference is the scale vs frequency. If only dyadic wavelet transform is performed, the frequency band is divided as [fs/4 fs/2], [fs/8 fs/4], [fs/16 fs/8]... whereas the frequency is sampled evenly in STFT. So if you want to get a even frequency sampling in scalogram, you can't use the dyadic sampling. NI will provide an analytic (complex, continuous) wavelt transform in next wavelet toolkit release. It can perform the traditional scalogram and the STFT comparable scalogram.
NISH DSP
