On the Frequency Response of Sampled-Data Systems

Earlier work on sampled-data theory has extended the powerful technique of frequency response analysis to discrete systems. It is shown in this paper that the development to date has been inadequate in explaining the behavior of sampled systems under sinusoidal excitation. For purely discrete systems, replacing s with jω in Laplace and Z forms is satisfactory. However, for discrete-continuous systems, a more complete analysis is necessary. In the present work, impulse sampling is considered as a suppressed carrier modulation process where input sinusoidal components appear as sidebands about the sampling frequency and all of its integer multiples. Thus, signal behavior at the output of continuous elements may be interpreted in terms of these spectral components. This approach provides a deeper insight into the sampling process and raises some interesting questions about the meaning of frequency response.