Mark Wickert

Signals and systems is an aspect of electrical engineering that applies mathematical concepts to the creation of product design, such as cell phones and automobile cruise control systems. Absorbing the core concepts of signals and systems requires a firm grasp on their properties and classifications; a solid knowledge of algebra, trigonometry, complex arithmetic, calculus of one variable; and familiarity with linear constant coefficient (LCC) differential equations.

You probably have some level of familiarity with consumer electronics, such as MP3 music players, smartphones, and tablet devices, and realize that these products rely on signals and systems. But you may take for granted the cruise control in your car. Here, the signals and systems framework in three familiar devices are shown at the block diagram level — a system diagram that identifies the significant components inside rectangular boxes, interconnected with arrows that show the direction of signal flow.

Following are eleven signals and systems concepts that apply to the design of a signal processing system known as an audio graphic equalizer. When you listen to music on a portable music player or a computer, you can usually customize the sound— you can re-shape the frequency spectrum of the underlying music signal to suit your tastes using a set of ten tone controls.

For many people in the United States, AM radio — a legacy modulation scheme known as amplitude modulation (AM) — is the place to go for talk radio and sports. But AM is more than just commercial broadcasting. Aircraft use AM to communicate with the tower at an airport, and shortwave radio uses AM for international broadcasting.

Discrete-time signals and systems march along to the tick of a clock. Mathematical modeling of discrete-time signals and systems shows that activity occurs with whole number (integer) spacing, but signals in the real world operate according to periods of time, or the update rate also known as the sampling rate.

Sampling theory links continuous and discrete-time signals and systems. For example, you can get a discrete-time signal from a continuous-time signal by taking samples every T seconds. This article points out some useful relationships associated with sampling theory. Key concepts include the low-pass sampling theorem, the frequency spectrum of a sampled continuous-time signal, reconstruction using an ideal lowpass filter, and the calculation of alias frequencies.

Both signals and systems can be analyzed in the time-, frequency-, and s- and z-domains. Leaving the time-domain requires a transform and then an inverse transform to return to the time-domain. As you work to and from the time domain, referencing tables of both transform theorems and transform pairs can speed your progress and make the work easier.

The study of signals and systems establishes a mathematical formalism for analyzing, modeling, and simulating electrical systems in the time, frequency, and s- or z-domains. Signals exist naturally and are also created by people. Some operate continuously (known as continuous-time signals); others are active at specific instants of time (and are called discrete-time signals).

Signals — both continuous-time signals and their discrete-time counterparts — are categorized according to certain properties, such as deterministic or random, periodic or aperiodic, power or energy, and even or odd. These traits aren't mutually exclusive; signals can hold multiple classifications. Here are some of the most important signal properties.