In this paper we have proved that the solution of parabolic equation and its Fast Fourier Transform generate continuous wavelet transforms. Indeed, we have solved the parabolic equation using PDETool, exported its solution and coefficients to Matlab workspace. We have then imported the solution from workspace to signal processing tool. We have sampled the imported solution with the sampling frequency of 8192Hz and applied the band pass filter with that frequency. The convolution of the sampled PDE solution with the impulse response of the band pass filter has generated wavelet transform. This algorithm computes the wavelet transform either directly of via Faster Fourier Transform. The computation of the FFT of the PDE solution has produced complex wavelet.