A window into the frequency domain, part 2
Jit Lim - May 23, 2012
From guest blogger Gina Bonini: In my last post, I reviewed windowing factors used during scope FFTs—why they’re needed, and how to select the right one. In this post, I’ll continue down the path of reviewing key tidbits about the scope FFT function, an often confusing and somewhat mysterious topic.
One of the biggest concerns when performing an FFT is aliasing. Aliasing occurs when the scope doesn’t sample the signal fast enough to accurately capture the higher-frequency components of the signal. When an FFT is then performed, those higher frequencies will appear as lower frequencies or aliases. Below is an example of an aliased waveform in the time domain.
The greatest frequency that can be input into a sampler (e.g., your scope) without aliasing is 1/2 of the sample frequency. Even if your signal has a fundamental frequency less than 1/2 your scope’s sample rate, you need to also be wary of the harmonics of your fundamental or, if you have a complex waveform, the higher-frequency components of your signal. Those higher-frequency components may be greater than 1/2 the sample rate, and they will alias. This shows up in the FFT as frequencies that fold back into the display.
Here are three methods for identifying aliases if they occur:
1. Fast-rising edges in a waveform create many high-frequency harmonics. These harmonics typically decrease in amplitude as their frequency increases. The figure below shows how these harmonics fold back into the display at the Nyquist point and are easily identified.
2. A second way to identify the aliases is to select the channel on which the FFT is being applied and increase the sample rate by turning the horizontal scale knob. This will increase the Nyquist frequency point and cause the aliased signals to unfold and no longer be aliased. The figure below shows how the signal from the previous example would unfold as a result of adjusting the sample rate.
3. Lastly, adjust the input signal’s frequency, if possible. As the input frequency is increased, the non-aliased harmonics will move toward the right-hand side of the screen. However, the aliased harmonics will move toward the left. This is show in the figure below.
Note that it is also possible for the aliases to move toward the right. As the input signal’s fundamental frequency is increased, the aliases move toward the left of the screen. When they reach the edge, they will reflect back into the display and begin moving toward the right again.
Here’s one more tip: You can use the scope’s bandwidth limit filter to filter out (or at least attenuate) higher frequencies and minimize aliasing.
In my next post, I’ll take a look at what sample length is needed to generate the spectrum you need. It’ll be an exciting tale of resolution bandwidth, windowing factors, and a few other dizzying terms, so don’t miss it!
Gina Bonini is a technical marketing manager for Tektronix. She has worked extensively in various test-and-measurement positions for more than 15 years, including product planning, product marketing, and business and market development. She holds a BSChE from the University of California, Berkeley, and an MSEE from Stanford University.