What's Your Point of View?
Time, frequency and modal domains offer complementary views, insight
Each of us is a critical-thinking problem solver. We have to be, as society's problems are mounting, getting harder, broader, deeper and multidisciplinary. As basic engineering skills — analysis, hardware and software — have become commodities worldwide, America's competitive advantage comes from being immediate, innovative, integrative and conceptual. Our innovation must be local — you can't import it, you create it! It is a way of thinking, communicating and doing. It differentiates us from other engineers around the world.
As multidisciplinary teams are formed to solve these problems, usually with a core group comprised of mechanical, electronic, computer and controls engineers, together with problem-specific experts in, for example, combustion, chemistry, structures, materials, anatomy and physiology, insight and communication are of utmost importance. We have all witnessed how engineers from different backgrounds describe the same concepts using different language and different points of view which often can lead to confusion and ultimately design errors. Being able to describe concepts, with clarity and insight, in a variety of ways is essential for the mechatronics engineer as the multidisciplinary team leader.
Relationship between Time and Frequency Domains
The two domains — time and frequency — represent different perspectives. They are interchangeable, complementary points of view, i.e., no information is lost in changing from one domain to another, and together lead to better understanding and insight.
Most signals and processes involve both fast and slow components happening at the same time. In the time domain (temporal) we measure how long something takes, whereas in the frequency domain (spectral) we measure how fast or slow it is. No one domain is always the best answer, so the ability to easily change domains is quite valuable and aids in communicating with other team members.
A third domain, the modal domain (not discussed here) is particularly valuable in analyzing the behavior of mechanical structures. It breaks down complicated structural vibration problems into simple vibration modes. Unique insight into the use of the modal domain in mechatronic system design has been provided in the work of Dr. Adrian Rankers, manager of Mechatronics Technologies, Philips Applied Technologies.
The time domain is a record of the response of a dynamic system as indicated by some measured parameter, as a function of time. More than 100 years ago, Jean Baptiste Fourier showed that any real-world signal can be broken down into a sum of sine waves and this combination of sine waves is unique. By picking the amplitudes, frequencies and phases of these sine waves, one can generate a waveform identical to the desired signal. To show how the time and frequency domains are the same, the figure shows three axes: time, amplitude and frequency. The time and amplitude axes are familiar from the time domain. The third axis, frequency, allows us to visually separate the sine waves that add to give us the complex waveform. Note that phase information is not represented here.
If we can predict the response of a system to a sine wave input, i.e., the frequency response, then we can predict the response of the system to any real-world signal once we know the frequency spectrum of that signal. The system's frequency-response curves are really a complete description of the system's dynamic behavior.
Engineers who can bridge gaps among disciplines and articulate complementary points of view clearly and insightfully will certainly have a competitive advantage.