Spectral analysis provides the frequency information of the data. Fourier tansform projects the data from time domain into frequency domain, while the time information is completely lost after the procedure. Time-frequency analysis is a procedure to localiza the frequency content in time. Wavelet transform is a method to do the time-frequency analysis of the data. Many methods of wavelet transform have been developed such as the continuous wavelet transform, the multiresolution analysis, the wavelet packet and the matching pursuit decomposition. Each method has its own advantages of providing a time-frequency representation of the data. In the thesis, different methods of wavelet transform are introduced and performed on different data. The advantages and the disadvantages of different methods are analyzed so that different methods of wavelet transform could be applied in different situations. In practice, different methods should be used together to provide an good time-frequency representation for different data.