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 in Figure 1 is a sample. 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,2
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 is 35,000 and altitude is 27,000. Note that the indexes start from zero. The first sample is at index 291, the second sample is at index 1, the third at index 2, and so on.