This thesis gave emphasis to the synthesis and design of the filters with transmission zeros. And studied related theories and technologies.Firstly, the synthesis and design of the conventional filters (Butterworth、 Chebshev、 cauer) and frequency transformation was given as the basic theory; Further more, the general Chebshev filters with transmission zeros was introduced, and a method to extract multi transmission zeros of general Chebyshev filters was presented; Then the general Butterworth filters was br...