Two digital methods are proposed for the solution of the time-domain approximation problem. Tho first method, based on a reeursivo algorithm for tho matrix pseudo-iriverso, determines the pulse transfer function of a discrete-timo system of a prescribed order providing the best fit in tho least squares sense at tho samplo points. Tho continuous-time system transfer function is then derived by using a simple transformation provided that tho sampling frequence oxeeeds tho Nyquist rate. Tho method is direct and computationally efficient. The second method is based on using an offieiont gradient search algorithm providing the best fit in the leastpti sense at tho samplo points. A number of examples illustrato the methods