What's Your Frequency?

Raw data from a pressure or temperature sensor may let engineers quickly spot trends. Such time-domain data often allows for an intuitive understanding of how equipment responds to testing or to everyday use. But often, analysis requires crossing into the frequency domain to unlock useful information from data acquired while testing rotating machinery, vehicles, communication systems, and other dynamic systems.

Mention "frequency domain" to an engineer and Fourier analysis immediately comes to mind, as does the fast Fourier transform (FFT). Many spreadsheets and data analysis packages provide FFT routines that can extract frequency information from large files of test data.

The spectrum of FFT tools also includes a "zoom FFT" that can focus on a band of frequencies. This technique performs only the FFT calculations needed to obtain data about frequencies in a narrow range of interest. Many digital communications methods produce such narrow band signals. The zoom FFT also finds use in Doppler radar, mechanical stress analysis, and medical ultrasonic imaging.

But an FFT works best on signals that maintain a constant frequency "composition" during the sample period. If frequencies in a signal vary during sampling, an FFT may produce erroneous results. And, an FFT cannot provide time information—that is, what happens to a signal at a specific time.

When analysis involves signals with varying frequencies, engineers can apply joint time-frequency analysis (JTFA) tools to extract information. These tools rely on a short-time Fourier transform (STFT) and a Gabor expansion, the inverse of an STFT. The STFT performs an FFT sequentially on small sections of data to produce spectral information as it existed in a signal at a specific "instant." For an STFT to yield useful results, only small frequency changes can occur during the short sampled period. JTFA tools have an added benefit—they generally reduce the influence of noise on signals.

Additional tools that provide frequency-domain information include wavelet analysis, which uses software filters to separate a signal into frequency bands. Unlike an FFT, wavelet analyses preserve timing information that shows how frequency content changes with time. In addition, a wavelet transform simultaneously extracts both low-frequency and high-frequency signals, but with different frequency resolutions—an advantage over the FFT. An inverse wavelet transform will reconstruct the original signal.

Wavelet analysis also provides for signal matching. If you expect to find a signal with known characteristics in your data, you can insert that signal's wavelet into the transform and confirm the presence or absence of the known signal.

Engineers also may apply order analysis to help them relate frequency-domain information to physical test systems. When you test a mechanical system, for example, each component has its own resonant frequency. So, while testing an 8-cylinder internal-combustion engine, a frequency eight times that of another may provide useful information about cylinder firing. "Order" simply means integer multiples, also called harmonics or overtones, of lower frequencies.

More Tools

Commercial signal-processing software includes many other frequency-analysis tools such as octave analysis, modal analysis, power spectrum, adjacent-channel power, harmonic distortion, and so on. But which tools apply to a specific test?

Before engineers attach transducers and sensors to equipment, they should know what information they need to analyze. It may seem obvious, but without understanding measurement needs, there's no way to know what sensors to apply or where to put them.

Test engineers unfamiliar with equipment must ask, "What does this device do, and what do we want to know about it?" They don't need to understand all the low-level details, but they must know what information their colleagues expect a test to yield so they can determine the types of analysis tools to use.

Adept Use

Do not apply data-analysis tools blindly. Excessive filtering, for example, may remove the specific signal you want to observe. On the other hand, lack of some sort of noise reduction may ruin your final information.

Thankfully, engineers often save data and then investigate it later so they have the opportunity to try different processing tools and see their effects. These trials provide practical training in what the tools do and don't do, and when to apply them.

Say you apply a window function prior to running an FFT and the results still lack sharp frequency bands. A bit of experience will suggest that signal frequencies changed during sampling. So next you try a joint time-frequency analysis to see if the results improve. Experimenting with known data will help you learn how to move from the time to the frequency domain and still get useful results.