Time domain design of stable recursive digital filters

An iterative technique is developed which can be used to determine an approximation to a linear system from a finite number of samples of its impulse response. The approximation is derived on the basis of the least squared-error between the desired impulse response and the impulse response of a recursive filter model. The unique advantage of the technique is that the model response is constrained to be in space, by augmenting the given impulse response with a particular square summable sequence that not only guarantees stability, but enables the solution of a constrained minimization problem. An algorithm to mechanize the technique was programmed in FORTRAN, and used on stable and unstable system responses to illustrate the technique.