Discrete–time Fourier Series and Fourier Transforms

We now start considering discrete–time signals. A discrete–time signal is a function (real or complex valued) whose argument runs over the integers, rather than over the real line. We shall use square brackets, as in x[n], for discrete–time signals and round parentheses, as in x(t), for continuous–time signals. This is the notation used in EECE 359 and EECE 369. Discrete–time signals arise in two ways. Firstly, the signal could really be representing a discrete sequence of values. For example, x[n] could be the n digit in a string of binary digits being transmitted along some data bus in a computer. Or it could be the maximum temperature for day number n. Secondly, a discrete–time signal could arise from sampling a continuous–time signal at a discrete sequence of times.