The basics of DSP for use in intelligent sensor applications: Part 1In earlier articles on intelligent sensor design, we saw how valuable they can be to both end users and those who manufacture and sell them. It’s now time to delve more deeply into what it takes to make intelligent sensors work.
The first step in that journey is to develop a solid, intuitive understanding of the principles of digital signal processing(DSP). Unlike many introductory DSP articles and texts, the focus here will be on presenting and using the important concepts rather than deriving them, for the simple reason that addressing the subject in depth is a book-sized, not a chapter-sized, project.
Other authors have already done an excellent job of addressing the topic in a more rigorous manner,1 and our goal here is not to try to condense their work to meaningless bullet points but rather to understand how to use certain key concepts to turn raw sensor data into meaningful sensor information.
By the end of this series, the reader should be comfortable identifying the key signal processing requirements for typical applications and be able to determine the appropriate process for extracting the desired measurements.
Although this discussion of DSP isn’t as rigorous as most academic treatments of the subject, it’s essential that we establish a clear understanding of several key concepts that form its foundation.
Beginning with precise definitions of what we mean when we refer to “signals” and “noise,” the discussion moves into the analysis of signals in both the time and frequency domains and concludes with an introduction to filtering, a technique that is commonly used to extract the desired information from noisy data.
What We Mean by Signals and Noise
The dictionary defines the term “signal” as “an impulse or fluctuating electric quantity, as voltage or current, whose variations represent coded information,”2 and this definition serves well as a starting point.
One interesting characteristic of electronic signals is that they operate under the principle of superposition. This principle states that the value of two or more signals passing through the same point in the same medium at a particular point in time is simply the sum of the values of the individual signals at that point in time.
For example, if we had N different signals, the resulting signal is the superposition of the N signals and would be represented mathematically as:
It turns out that the principle of superposition is a very powerful tool; using it, we can often deconstruct complex sensor signals into separate, more basic components, which may simplify the analysis of the problem and the design of the resulting system.
Many real-world sensor examples make extensive use of this principle in the creation of the appropriate signal-processing techniques for each specific application, but first let’s examine one way in which superposition leads to a better understanding of all sensor signals.
Consider the circuit shown in Figure 2.1a below, which contains a thermocouple connected to a voltmeter in an idealized environment. As discussed in earlier articles, the thermocouple produces an analog output voltage VT(t) that varies over time t with the temperature of the thermocouple junction.
In this case, the measured signal VM(t) is simply the “true” signal VT(t) and the information coded in it is the temperature of the thermocouple junction.
|Figure 2.1a. Basic Idealized Thermocouple Circuit|
Unfortunately, such an idealized environment exists only in our imaginations, much like a perfectly silent library exists only in a librarian’s fantasy. Just as even the quietest library has some audible noise, real-world circuitry contains electronic noise that comes from both the surrounding environment and the components used to create the circuit.
Thus, a more accurate representation of the basic thermocouple circuit would include an electrical noise generator that produces a noise voltage component VN(t) superimposed on the “true” thermocouple signal VT(t), as is shown in Figure 2.2a below.
|Figure 2.2a. More Realistic Thermocouple Circuit Model with Noise|
To an outside observer, this distinction is not actually discernible; they simply see the measured voltage VM(t) that contains both components and is equal to:
Of course, the end user generally doesn’t want the noise component to be a part of the measured signal; after all, he’s interested in the “true” thermocouple signal that has the information of interest, not a corrupted signal that distorts that information.
Depending upon the characteristics of the signal of interest and of the noise, it can be possible to accurately extract the signal of interest even in the presence of significant levels of noise using the techniques to which we will now turn.