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Analyzer Mythbusting: Clearing Up Common Points Of Confusion With Dual-Channel FFT Analyzers

Clarifying “FFT vs RTA vs transfer function” along with “frequency response vs magnitude response” and several other areas sometimes misunderstood.
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The wonderful silver lining of our present situation is that the internet is being flooded with all sorts of seminars, online classes, training videos, and the like. I’ve got a bunch of stuff bookmarked to dive into and it feels a bit like trying to drink from a firehouse.

However, I’ve stumbled across a few resources that seem to have some wires crossed regarding measurement theory and audio analyzers, so let’s take a minute and address some of the common mixups I’ve seen with regards to [Rational Acoustics] Smaart as well as other dual-channel FFT analyzers.

“FFT” Vs “RTA” Vs “TRANSFER FUNCTION”
Many resources conflate these terms. Here’s the scoop: FFT stands for Fast Fourier Transform, which is a mathematical operation that transforms time-domain data into frequency-domain data. In other words, FFT tells us what frequency components make up a signal.

Regardless of whether you’re taking an RTA or a Transfer Function measurement with an analyzer, the FFT is what’s happening under the hood to generate that data.

So trying to draw a comparison like “FFT vs RTA” is sort of like saying “Internal combustion engine vs Dodge Charger.” It makes a bit more sense to discuss RTA vs Transfer Function measurements, but both use FFT under the hood.

“FREQUENCY RESPONSE” Vs “MAGNITUDE RESPONSE”
The terms “magnitude response” and “frequency response” are often used interchangeably; however this is shorthand and it’s good to be clear on what we really mean for the sake of the folks who might not know the difference – kind of like that whole phase/polarity thing.

The magnitude response measurement displays magnitude over frequency, and the phase response measurement shows phase over frequency. The phase trace is a frequency-domain measurement as well, so in this context, the term “frequency response” collectively refers to both magnitude and phase over frequency. (Mathematicians use the term “Bode plot,” named for American engineer Hendrik Wade Bode, to describe this type of graph showing the frequency response of a system in magnitude and phase. Keep that one handy for the Sunday crossword.)

DATA WINDOW FUNCTIONS
Contrary to some claims, data window functions aren’t used to “fix rounding errors” or “infinitely repeating” decimal values. Here’s the deal: the textbook Fourier transform has a continuous frequency response running from 0 to infinity (DC to light, if you want to think of it that way).

However, in order for that to work, T = 1/f tells us that the input signal must also be infinitely long (or, in a more strictly mathematical sense, “continuous and aperiodic”). It’s not going to work too well for our purposes because we have sound check in an hour. So audio analyzers employ a Discrete Fourier Transform (DFT), which uses just a chunk of an input signal (which we call the Time Record or Time Window) and assumes that it’s infinitely repeating in a similar fashion. If you listen to a four-bar drum loop in your DAW, you know it will sound the same even if you loop it forever.

(“But wait,” you might think. “What’s all this “Discrete” nonsense? I thought they used Fast Fourier transforms.” The “Fast” bit is just a specific version of the DFT that can be calculated more efficiently, which is what allows us to carry out the analysis in real time. So FFT is just a special flavor of DFT.)

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However, the whole “infinitely repeating” bit is an assumption that’s not true with real-world audio signals. If you’ve ever built loops in a DAW, you know the snap/crackle/pop nasties that are created by a bad loop edit. This causes a bunch of noise and error in the measurement that manifests by signal content at one frequency “bleeding” into the other frequency data points. Figure 1 shows how a 500 Hz sine wave spills over into the full spectrum of the measurement bandwidth.

Figure 1

Enter the data window. If we “fade in” at the beginning out our selected signal chunk and “fade out” at the end, we’ve made the “infinitely repeating” assumption “more true,” because the end matches the beginning. That lets the DFT do its job with an input signal that matches its expectations. Figure 2 depicts the same measurement taken with a data window applied.

Figure 2

The spillage is greatly reduced, giving us a much cleaner measurement. There are a bunch of different data window options in most modern analyzers, but the default settings tend to be carefully chosen to give great results out of the box and shouldn’t require any tweaking in most situations.

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