Sampling and Reconstruction of Continuous-Time Signals

Abstract This chapter presents the theory for transferring a continuous-time signal into its discrete-time form by sampling, and then converting the obtained samples to a digital signal suitable for processing in a processing machine, using the procedure of sample quantizing and coding. Then, the procedure of converting a digitally processed signal into discrete signal samples and the reconstruction of the initial continuous-time signal via a lowpass reconstruction filter is presented. The theory provides the mathematical base for both analogue-to-digital and digital-to-analogue conversions, which are extensively used for processing signals in discrete communication systems. The chapter goes on to show that the Nyquist criterion must be fulfilled to eliminate signal aliasing in the frequency domain. Finally, the mathematical model for transferring a continuous-time signal into its discrete-time form, and vice versa, is presented and demonstrated for a sinusoidal signal.