This example shows how to improve the frequency-domain accuracy of a system with a time delay that is a fractional multiple of the sample time.
For systems with time delays that are not integer multiples of the sample time, the Tustin and Matched methods by default round the time delays to the nearest multiple of the sample time. To improve the accuracy of these methods for such systems, c2d can optionally approximate the fractional portion of the time delay by a discrete-time all-pass filter (a Thiran filter). In this example, discretize the system both without and with an approximation of the fractional portion of the delay and compare the results.
Create a continuous-time transfer function with a transfer delay of 2.5 s.