Books and Articles by 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.

A signal is classified as deterministic if it’s a completely specified function of time. A good example of a deterministic signal is a signal composed of a single sinusoid, such as with the signal parameters being: A is the amplitude, f0 is the frequency (oscillation rate) in cycles per second (or hertz), and is the phase in radians.

Computer and electrical engineers work through a process that allows them to test, or model, potential solutions to find out whether the idea is likely to work in the real world. For products that rely on signal processing, engineers use signals and system modeling and analysis to reveal what’s possible. When you’re trying to quickly prove a solution approach, you’ll often turn to behavioral level modeling of certain elements of the overall system to avoid low-level implementation details.

The ZT doesn’t converge for all sequences. When it does converge, it’s only over a region of the z-plane. The values in the z-plane for which the ZT converges are known as the region of convergence (ROC). Convergence of the ZT requires that The right side of this equation shows that x[n]r-n is absolutely summable (the sum of all terms |x[n]r–n| is less than infinity).

Signals, both continuous and discrete, have attributes that allow them to be classified into different types. Three broad categories of signal classification are periodic, aperiodic, and random. Periodic signals Signals that repeat over and over are said to be periodic. In mathematical terms, a signal is periodic if x(t + T) = x(t) (continuous-time) x[n + N] = x[n] (discrete-time) The smallest T or N for which the equality holds is the signal period.

A type of signal classification you need to be able to determine is periodic versus aperiodic. A signal is periodic if x(t) = x(t + T0), where T0, the period, is the largest value satisfying the equality. If a signal isn’t periodic, it’s aperiodic. When checking for periodicity, you’re checking in a graphical sense to see whether you can copy a period from the center of the waveform, shift it left or right by an integer multiple of T0, and if it perfectly matches the signal T0 seconds away.

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.

Continuous-time signals and systems never take a break. When a circuit is wired up, a signal is there for the taking, and the system begins working — and doesn’t stop. Keep in mind that the term signal is used here loosely; any one specific signal may come and go, but a signal is always present at each and every time instant imaginable in a continuous-time system.