Fourier Transform

Fourier Transform is well developed transformation theory with lots of approximation. In Fourier Transform, signals in time domain is transformed to frequency domain which can give frequency information about signal occurred without time information that is Fourier Transformation can not give time range or time of occurrence of particular signal or band of signals.

To get the time information, STFT is introduced with approximation in signal resolution because of width of windowing function. Because of windowing function some of important information in the signal may be lost if the information content frequency signal is out of integration range of window function.If the windowing function has small width it will have good time resolution but poor frequency resolution and have poor time resolution and good frequency resolution at large windowing function width as stated in Heisenberg Principle.
To overcome these resolution problems of varying windowing function, wavelet transform is introduced which maps the time signal into frequency-time domain. Because of changing window size of analysis function, Wavelet Transform gives good frequency resolution at lower frequency range and good time resolution at high frequency range.