Random Samples

Abstract

When a binary signal, which takes values 1 and — 1, is transmitted through a noisy channel and corrupted by electrical, thermal, and other disturbances, the signal changes erratically. The received signal is sampled at a certain interval, the values of the samples range any where from — 1 to 1 and even sometimes less than — 1 and greater than 1. These samples are called random variables, because the values of these samples are unpredictable. The binary signal, its corrupted version, and samples are shown in Fig. 2.0–1. The recorded signal in an electrocardiagram is random due to the uncertain behavior of the heartbeat. The samples of this signal taken at a certain uniform interval are random samples. The return of a radar signal from a target is a random signal and, the samples of this signal take random values. In optical communications, the number of photons received in a photodetector during a certain interval is a random number. The number of time-sharing terminals accessing a main frame at any particular time is a random number. If a coin is flipped 10 times, the number of heads that come up is a random number, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, or 10. If a die is thrown, the number that appears on the top is a random number, 1,2, 3,4, 5, or 6. If the outcome of an experiment cannot be predicted with certainty, the experiment is called a random experiment and the outcome is called a random event. If the observed or received signal from a channel or sensor system is unpredictable, the signal is called a random signal.