Signals and Systems For Dummies
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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. For example, a subsystem design may require knowledge of a signal parameter (such as amplitude or frequency) to function.

At first, you may assume that the parameter is well known. Later, you add low-level details to estimate (not perfectly) the parameter. As your confidence and understanding grows, you represent the low-level details in the model and actual implementation becomes possible.

Behavioral level modeling also applies when you need to model physical environments that lie outside a design but are needed to evaluate performance under realistic scenarios.

Staying abstract to generate ideas

Behavioral level modeling isn’t void of hardware constraints and realities, but it requires a certain level of abstraction to allow preliminary concept solutions to materialize quickly. Behavioral level models depend on applied mathematics.

In other words, computer and electronic engineers don’t frequently handle actual hardware and devices used for an implementation. The model of the hardware is what’s important at this point. The engineer’s job is to conceptualize systems and subsystems through a framework of mathematical concepts, and abstraction provides great creative freedom to explore the possibilities.

Suppose you seek a new design for an existing system to improve performance. You hope to make such improvements with new device technology. You don’t want to get bogged down in all the details of how to interface this device into the current design, so you move up in abstraction with a model to quickly find out how much you can improve performance with a new design.

If adequate improvement potential doesn’t exist, then you settle down and investigate other options. Rinse, lather, and repeat.

Keep in mind that improved performance isn’t always the primary objective of signals and systems modeling. Sometimes, a design is driven by cost, availability of materials, manufacturing processes, and time to market, or some other consideration.

Working from the top down

A design that relies on signals and systems starts from a top-level view and works down to the nitty-gritty details of final implementation. Analysis and simulation performed at the top level depends on behavioral level modeling. The model is ultimately broken into subsystems for testing and refinement, and then the system comes together again before implementation.

Typically, your task as an electronic engineer is to create some new or enhanced functionality for a computer- or electrical-based product. For example, you may need to support a new radio interface due to recent standard updates.

At first, the changes may seem simple and straightforward, but as you dig into the work, you may begin to see that the changes require significant adjustments in signal processing algorithms. This means that the new radio interface will require a few totally new designs, so you need to model and simulate various implementation approaches to find out what’s likely to work best.

Relying on mathematics

Many people write off signals and systems as a pile of confusing math, and they run for the hills. True, the math can be intimidating at first, but the rewards of seeing your finely crafted mathematical model lead the way to a shipping product is worth the extra effort. In the end, the math is on your side. It’s the only way to model concepts that function properly in the real world.

A go-to approach when a problem seems unsolvable: Take it slow and steady. If a solution isn’t clear after you think about the problem for a while, walk away and come back to it later. Practice and experience with various problem-solving techniques and options help, so try to work as many types of problems as you can — especially in the areas you feel the most discomfort. Eventually, a solution reveals itself.

When possible, verify your solutions by using computer analysis and simulation tools such as Python with the numerical support and visualization capabilities of PyLab (NumPy, SciPy, matplotlib) and the IPython environment to perform number-crunching analysis and simulations. For problems involving more symbolic mathematics, use the computer algebra system (CAS) provided by Maxima.

About This Article

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About the book author:

Mark Wickert, PhD, is a Professor of Electrical and Computer Engineering at the University of Colorado, Colorado Springs. He is a member of the IEEE and is doing real signals and systems problem solving as a consultant with local industry.

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