Continuous wavelet transform and exactly solvable model of nonstationary signals

An analytic expression for a continuous wavelet transform (CWT) is obtained for a nonstationary signal with spectral properties varying with time. As a model of the nonstationary signal, a superposition of elementary nonstationary signals is considered, each of which is the product of the Gaussian-shape envelope and an oscillating function. To obtain the CWT, the mother Morlet wavelet is used. The result is compared with the window Fourier transform (Gabor transform).The advantages of the CWT are illustrated by concrete examples. The applications of the exactly solvable model of nonstationary signals for simulating transient processes in physics are considered.