Sampling is the key procedure for the digital processing of analog signal. In recent years, signal processing methods employing traditional sampling mechanism have faced tremendous challenges due to the rapid growth of signal bandwidth and information transmission rate, and some new signal processing technology such as the wavelet transform and the compressed sensing emerged at the right moment. On this occasion, it is necessary to reexamine the classical Shannon-Nyquist sampling theorem in theory, and study universal expression, sampling and reconstitution theory of signal. The nature of signal expression is analyzed from the point of view of signal projection and function representation. Firstly, the Shannon traditional sampling and reconstruction theory, and the generalized sampling and reconstruction theory proposed by Papoulis and extended by Unser are introduced. Then, the consistency between modern signal processing and transforming methods (wavelet transform, compressed sensing) and generalized sampling theory is investigated mathematically. Meanwhile, the chirp signal is taken as a simulation example to illustrate the relationship between signal sampling and reconstruction, as well as the similarities and differences in each method.