for gmsk modulation let f t denote the impulse response of f s f ref furthermore let g t denote the desired pulse shaping for the gsm system we have equ3 where the function rect x is defined by equ4 and the operator 34 34 denotes convolution also a t is defined by equ5 in order to have a convenient description of the design procedure the previously mentioned quantities are sampled with a sampling rate equal to 1 t and a matrix formalism is used to represent the signals let h denote an l u00d7 1 vector which represents the impulse response of the compensated pulse shaping let f denote an n u00d7 1 vector containing f tk for k 0 1 2 n 1 and let g denote an n u00d7 1 vector containing g tk 3 2t b for k 0 1 2 n l 2 a convolution matrix f of dimension n l 2 u00d7 l can now be constructed from f as equ6 and the design problem can be formulated using matrix notations as follows the overall pulse shaping is given by fh the desired pulse shaping is given by g the problem is to find an h so that fh is as close to g as possible one important characteristic of g is its static gain this is because a deviation from the correct static gain may cause the phase of the vco 604 to drift in this description we consider the criteria equ7 subject to equ8.