Discrete Time Sampling and Processing
Fatos Tunay Yarman Vural, Emre Akbas · 2024
Abstract This chapter extends the continuous time sampling theorem of C. Shannon into discrete time signals and systems. We study the methods for down-sampling the discrete time signals. We explain the constraints imposed by the discrete nature of signals in time and frequency domains: the sampling period is restricted to be integer-valued, and as we sample the signal with a period larger than 1, we define a new signal, where we insert 0 values in between the integer multiples of the sampling period. We restrict the signal to be band-limited with the cutoff frequency. We show that a discrete time signal can be down-sampled with the sampling frequency, which is at least equal to the Nyquist rate, without losing any information. The reconstruction of a sampled signal is very similar to that of the continuous-time signals. All we need to do is to design a low-pass filter with the cutoff frequency of the band-limited signal.