Microprocessor-based simulation of sampled data systems with/without a hold device using a set of sample-and-hold functions and Dirac delta functions (Q1763982)

Linear dynamic systems are considered. A sampler is introduced. The output of the sampler is described by delta functions. A delta operational transfer function is defined. It consists of an upper triangular matrix with samples of the impulse response as elements. If \(m\) values of the time function are considered, an \(m\times m\) matrix is obtained. De facto the convolution integral is approximated by finite sums. If a sample-and-hold device is added, the delta functions must be replaced by differences of step functions. The method is used for calculating the step response in microprocessors. A first-order transfer function is presented as an example.