 Another design approach , particularly suitable for CAD because it is a numerical method , is to decompose the filter into a number of finite elements . These elements are a large number of simple steps and ridges . A number of methods are available to analyse the individual elements . The mode matching technique expands the field equations of the element into a series of eigenfunctions and then for each mode matches the field at the interface between elements . The Galerkin method expands the field equations into polynomial functions such as Gegenbauer polynomials or Chebyshev polynomials . These methods can be mixed according to what is convenient for a particular type of element . Whichever analysis method is used , the final output needed is the scattering parameters matrix for each element . The overall filter response is then found from the combined scattering matrix of all the individual element matrices . This method is analytic rather than synthetic , that is , a trial design must first exist in order to be analysed unlike synthesis methods where the starting point is a prescribed transfer function from which a design is synthesised . 
