Transfer Functions from Sampled Impulse Responses

A mathematical formulation is developed for obtaining the frequency responses from known sampled impulse responses of linear dynamical systems. This is done by assuming a straight line approximation from one sampled point to the next and performing the usual Fourier Transformation for this interval. This is repeated for all sampled points and the results are summed together. In practice sampled impulse responses can be obtained using correlation techniques. The frequency responses as obtained above are then processed by a generalised method, developed by the authors, to determine the transfer functions. The unique feature of this method is that the transfer functions can be obtained from the frequency responses without any idea about the actual order of the system and its poles and zeroes. However, the actual principle employed, that of complex curve fitting, is already a well established technique. Finally, many examples are presented which show the validity of the methods where impulse responses are exact and also corrupted by errors. The treatment is restricted to systems which have a finite dc gain. The numerical calculations are processed on an ICT 1905 computer.