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.

The great attributes of discrete-time signals and systems rely on the ability to interface with the continuous-time domain. Analog-to-digital converters (ADCs) and digital-to-analog converters (DACs) are the electronic subsystems that convert signals between continuous-time and discrete-time signal forms. This figure shows how to implement the interface of these two subsystems.

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.

Here’s a system-level look at the signals and systems model of a karaoke machine — an audio playback system with a powerful speaker that allows a person to sing over recorded music. A multimedia interface includes a TV to display and update lyrics as the music progresses. From a high-level signals and systems viewpoint, a particular design attribute of this system is that it contains a sensor, a microphone, and two audio transducers (the left and right channel speakers).

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.