Construction of a Morlet wavelet power spectrum

The Morlet wavelets transform (MWT) is an efficient means of detecting and analyzing transient signals. However, ordinary iterative processes that calculate the MWT are time-consuming. In addition, when the MWT is applied to construct a wavelet power spectrum on a linear frequency axis, the peak response appears at a value lower than the actual signal frequency. In this work, formulae that produce a fast MWT and Morlet power spectrum (MPS) scheme without iterative processes are derived. Also, we discuss in detail why the frequency slant phenomenon occurs. To avert this phenomenon, the transform kernel of the MWT is modified to facilitate the construction of an equal-amplitude Morlet wavelet transform. The modified Morlet power spectrum produces the peak responses roughly proportional to the squared input amplitudes at the accurate signal component frequencies.