System characterization by means of Impulse and Frequency Response Functions are well known in classical linear systems analysis. Impulse Response Function is a time domain description of a linear system where as the Frequency Response Function represents the frequency domain counterpart. Linear systems are often characterized in frequency domain. In many biological research applications, it becomes necessary to examine the impulse response function in order to understand the behavior of the system under investigation. One such application is the arterial system in cardiovascular dynamics. It has been shown that although both representations are identical, some aspects of the arterial system are better emphasized by one description than by the other. In order to obtain accurate estimates of the impulse response function it is desirable to solve the convolution integral in the time domain by deconvolving the system input and output time histories. Solution of the convolution integral is however extremely complex and requires the use of numerical approximation methods.

This work is primarily focused on developing these numerical approximation procedures with particular application emphasis on the arterial system.