When you periodically measure the value of some quantity, you’re sampling. Each one of your measurements is referred to as a sample. Discrete signals are simply lists of samples, and are usually generated by sampling real-world continuous signals.1 As an example, let’s think about the process of sampling the altitude of a plane over the course of a two hour long flight. In the following animation, we’ll generate a discrete signal by sampling the plane’s altitude every ten minutes.

Figure 1. Sampling the Altitude of a Plane During a Two Hour Long Flight

Each of the blue dots inis a. Instead of plotting our samples on a two-dimensional image, we might instead choose to represent our signal using a more conventional pen-and-paper type notation. In other words, we can represent our discrete signal as a simple list of numbers,

altitude = [291, 6000, 15000, 20000, 35000, 32000, 31000, 31000, 27000, 12000, 3500, 1200, 122]

We can refer to a particular sample by index. For example, altitude[4] is 35,000 and altitude[8] is 27,000. Note that the indexes start from zero. The first sample is at index 0, the second sample is at index 1, the third at index 2, and so on.