I am a beginner. The Fourier series, Fourier Transform and it's inverse play very important role in Fourier Analysis and Fourier Synthesis. I have read that Fourier transform is localised in only frequency domain.Also,it contains information about the signal in phase and frequency spectrum. Every approach has advantages and disadvantages. My question is what are disadvantages of 1.Fourier Analysis and 2.Fourier Synthesis compared to wavelets?