Transient response of sampled-data systems

IT IS KNOWN that the z-transform method¹⁻⁴ can be readily used for analysis and design of sampled-data systems. This method is essentially a Laplace transform technique in which the sampled output is related to the input by system functions in the form of z-transforms. These system functions can be generally regarded to consist of zeros and poles, in the form of rational polynomial in the variable z, where z is defined as ∊^Ts and T is the sampling period. The purpose of this digest is to investigate in detail the effect of the locations of the poles and zeros of the transfer function on the transient response of sampled-data systems when subjected to step input.