Last time out (here), we looked at early forms of audio measurement equipment, including chart recorders, heterodyne analyzers, and real-time analyzers (RTAs). Now let’s pick it up with fast Fourier transform analyzers (FFTs), which are still in widespread use the world over in a variety of forms.
In addition to accurately characterizing audio signals, FFTs are used for vibration analysis, order analysis of rotating machinery, RF and microwave measurements, and many other purposes. One could say they’re the gold standard of the test and measurement industry.
The capability of modern FFT analyzers runs deep, and they’re available in two distinct categories. The first is the “spectrum analyzer,” which measure the spectral response of a device-under-test (DUT), based either on a signal the device is emitting or by stimulating the device with a signal generated by the analyzer, or from another outside source. Spectrum analyzers are typically single-port machines; that is, they have only one input.
The second category is “network analyzers,” which are essentially a 2-channel spectrum analyzer with a calibrated source. They’re designed to compare the signal applied to the DUT on one port to the signal coming out of the DUT on the second port. By comparing the signals, the network analyzer detects any differences that are present in the arrival time and spectral content of the two signals. The act of comparing port 1 to port 2 is known as “transfer function.”
A Matter Of Time
FFTs are inherently time-based instruments; they capture a set of samples in the time-domain and then construct a variety of displays in the frequency-domain from the time data. Available displays typically include magnitude versus frequency (a.k.a., frequency response), phase versus frequency, group delay, coherence, and often much more, depending on the specific machine.
An industrial quality single-port spectrum analyzer, the Hewlett-Packard 3561A. (click to enlarge)
Signals not visible in the time domain, such as noise and distortion products, become clearly visible in the frequency domain.
It’s possible to view many different signals at the same time, because the spectral display shows the components that comprise the frequency response of the DUT distributed along the frequency axis. If we tried to look at pink noise, or a swept sine wave purely in the time-domain (as on an oscilloscope), we’d only see a jumble of traces that wouldn’t make any sense.
Modern FFTs often have enhanced capabilities. Many machines provide an inverse FFT measurement that can be used as a “delay finder.” In this mode the display will depict the difference in arrival time between the signal feeding port 1 and the signal feeding port 2, making it easy to determine the correct delay setting for an ancillary “delay” loudspeaker in a sound system.
FFTs are intrinsically linear. The display “points,” “lines,” or “bins,” as they’re called, are evenly divided across the spectrum-of-interest in the horizontal X-axis. They’re displayed as lines in some machines, or continuous traces that connect the tops of the lines together, in other machines.
While this can be very confusing at first – to look at a linear frequency display when you’re probably used to viewing logarithmic displays – it’s also very powerful. Rather than cramming 20 Hz to 20 kHz on to the display screen all at once, with limited low frequency resolution, significant qualitative value is had by limiting the frequency span to specific regions of interest.