Published on October 11, 2019

Copyright © **Dan P. Bullard**

I'll never forget the insane statements I heard coming from the mouths of engineers from one of the premier American test equipment manufacturers.

*"An FFT is just a button on a scope!"*

*"An FFT is just an approximation."*

How such truly stupid people could get a job, let alone, be employed for decades by one of the premiere 'scope makers in the world just astonishes me. If I ever said something like that in print I would be destroyed in seconds! But then I have to remember, some people don't have my intellect or experience. I was damn lucky. I was conceived with just the right combination of DNA to give me a pretty high IQ and a passion to learn all I could about the world. By contrast, my dad was an idiot. "Nobody knows how deep Lake Tahoe is." Really Dad? He said this after the USS Nautilus had gone *under* the North Pole, so, I kinda think they had the whole Sonar thing figured out. He was in the Navy too, but if he had been on Sonar and not selling extra leave time to his fellow sailors for cash, he might have learned something about the state of the art in electronics, physics and science in general. But, that was my lot in life. I grew up smart in a town full of idiots, so I am used to being surrounded by folks who know almost nothing about the world. But never did I think I would end up working for a company where the top engineers thought that an FFT was just an approximation. But then I realized, not everyone has had the opportunity to use a *coherent capture system* (pictured above).

After I got out of the Navy and spent two years teaching microprocessor electronics at a Silicon Valley tech school, I was recruited by GenRad to work on digital semiconductor testers. From there I moved on to Mixed Signal testers. I always capitalize Mixed Signal because to me, it's holy. It was a Godsend for sure. There I learned that the only proper way to capture a signal was to first source it with an Arbitrary Waveform Generator (AWG) using a clock to step through the samples in the AWG memory;

Then we use the same clock to capture the signal on the other side of the DUT (Device Under Test) and then to do an FFT to analyze it. If the digitizer couldn't keep up with the AWG, you could always divide down the clock, so for example, if you had one cycle of the wave in your AWG and you divided the clock by 5, say, you would end up with 5 cycles of the same wave in the capture instrument (as the AWG continuously loops on whatever is in its memory). This worked out damn well, because then you would do the FFT on the captured signal and the wave in question would appear in bin 5 of the spectrum and **only in bin 5**, and harmonics of the wave would end up in multiples of bin 5, 10 for the second harmonic, 15 for the third and so on. Put the sum of two waves in the AWG, say 1 cycle and 3 cycles, then digitize with a ratio of 5:1 clock speeds and the first signal would show up in bin 5, the second signal would show up in bin 15 and the first order intermodulation products would show up in 15-5 or bin 10 and 15+5 or bin 20. The key of this is the fact that **if** and *only if* the two instruments are clocked off the same time base, even if they are not at the same exact frequency, the FFT is perfect, with **no windowing needed**. Now, it wasn't hard to screw this up and get the math wrong so that you end up with a non-coherent capture, (which would scream window me!) but it wasn't that hard, and I got pretty good at doing the math to get the right answer, and I knew what the results looked like if you did it wrong, like this:

In this plot you can see that the energy in each frequency is spread out or *smeared* into neighboring spectral bins. But if you do it right, then you get something more like this:

So in a coherent capture where the clock driving the AWG is related to the clock driving the capture instrument each signal appears in a separate spectral bin. Again, if you don't get a beautiful spectrum like this, you did something wrong. I got used to that, and it became a sign to me that anyone who had a smeared spectrum was doing something wrong. And that includes anyone who thinks they have to window a wave after digitizing it and before doing an FFT on it. Now, it's true that if you capture a wave that doesn't come from an AWG, something that is created by a different clock source, unrelated to what your capture instrument is doing, then you don't have a lot of control. But that doesn't mean you are stuck doing windowing and turning our beautiful and extremely accurate FFT into an *approximation*.

There are ways to get around this. One was is pretty brilliant, it's based on a trick I did in using an FFT to measure duty cycle. You ascertain the exact frequency of the main signal in the wave under question, then do the math and use a Direct Digital Synthesizer (DDS) to set a clock frequency for your digitizer so that when you do the FFT, you are so close to being coherent that your FFT will never even notice that you are not. This is far better than windowing which seriously corrupts the resulting spectrum and makes otherwise descent engineers say stupid things about FFTs. The FFT is a perfect tool, I means **absolutely perfect**, but only if you feed it a coherent input. If you don't know what you are doing, you get smearing and then you have to window. And I will look down on you as an idiot who is just waiting his chance to say something insanely stupid. You have been warned.