Abstract: According to the features of signal to be processed, the wavelet transform is compared with short-time Fourier transform. It indicates that the wavelet transform is suitable for the processing of nonstationary and singular signal. The continuous wavelet transform, discrete wavelet transform and wavelet packet theory are reviewed in brief. Some key problems are discussed, such as sampling and fast algorithm which are essential to the application of wavelet transform. Finally, a data compression method is presented that compresses the raw SAR (Synthetic Aperture Radar) data by means of wavelet transform and vector quantizer. Compared with the traditional method, the result shows that the SAR image generated from compressed raw data has better SNR(Signal to Noise Ratio), and meanwhile the performance of wavelet transform in radar target identification and SAR image classification are also discussed.