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.

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.

Part of learning about signals and systems is that systems are identified according to certain properties they exhibit. Have a look at the core system classifications: Linearity: A linear combination of individually obtained outputs is equivalent to the output obtained by the system operating on the corresponding linear combination of inputs.

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).

Before getting into the closed-loop system function of the CD/DVD case study, consider a few attributes of the open-loop system function by writing it out, leaving Ka as the only variable not defined: You can find the pole-zero plot by using PyLab and custom function splane(b,a) found at ssd.py. This function returns the system function numerator and denominator polynomial coefficients as ndarrays b and a.

To finish off this case study, simulate the system in Python. To give you a feel for sinusoidal spectrum analysis and window selection, here’s a Python simulation that utilizes the test signal: Assume that the sampling rate is 10 kHz, which is greater than twice the highest frequency of 3,000 Hz. The first challenge is resolving the two equal amplitude sinusoids at 1,000 and 1,100 Hz (f = 100 Hz).

With the simplification to the open-loop system function in place, you can dive in and find the closed-loop system function of the CD/DVD case study, with full variable substitution. Here’s the closed-loop system function H(s) with the simplified open-loop system function applied: With Ka = 50, you have a natural frequency of 15.

Here are eleven common mistakes students make when trying to solve problems and how to avoid them. Slow down enough to think through solutions, and make sure your fundamental understanding of the core material is at least as good as your ability to work through detailed problems. Miscalculating the folding frequency In sampling theory, the alias frequencies fold over fs/ 2 (known as the folding frequency), where fs is the sampling frequency in hertz.