Filters are an essential part of telecommunications and radar systems and are key items in the performance and cost of such systems, especially in the increasingly congested spectrum. There has been a particularly marked growth in the cellular communications industry in recent years. This has contributed to both very demanding performance specifications for filters and the commercial pressures for low cost, high volume and quick delivery. Through an investigation into and a subsequent implementation of filter theory, the techniques to produce optimal filter performance for a class of filters are developed in this thesis. This thesis presents an entire design process for filter synthesis of narrow to moderate bandwidth filters, from an investigation of the basic theory through to the development of a generalised synthesis program. This program is an exact design method based on the concept of a matrix representation of coupling coefficients. The outline of the processes required to implement this method have been obtained from a paper by Cameron[1]. To develop the program, Cameron’s summary of the filter synthesis method has been expanded in detail, using further mathematical derivations to produce a Matlab program for generalised Chebyshev filter synthesis.A description of how to transpose the obtained mathematical results to the physical filter structure is included and a filter has been designed and made to specifications using the synthesis program. The process of tuning the filter via the group delay method, using results obtained mathematically is detailed. The overall process is verified by the results obtained from the physical filter.