The **FFT** (Fast Fourier Transform) first appeared when microprocessors entered commercial design in the 1970s. Today almost every oscilloscope from high-priced laboratory models to the lowest-priced hobby models offer **FFT** analysis. The **FFT** is a powerful tool, but using it effectively requires some study. I’ll show you how to set up and use the **FFT** effectively. We’ll skip the technical description of the **FFT,** because its already implemented in the instruments. Instead I’ll focus on the practical aspect of using this great tool.

The **FFT** is an algorithm that reduces the calculation time of the **DFT** (Discrete Fourier Transform), an analysis tool that lets you view acquired time domain (amplitude vs. time) data in the frequency domain (amplitude and phase vs. frequency). In essence, the **FFT** adds spectrum analysis to a digital oscilloscope.

If you look at upper trace in **Figure 1**, you’ll see an amplitude-modulated carrier that uses a trapezoidal pulse as the modulation function. If you look at the time-domain view in **Fig. 1** and I ask you to tell me the bandwidth of the signal, you’d have a hard time. But take the **FFT** of this signal and you get another point of view. The signal has a linearly swept frequency and the bandwidth, marked by the cursors, is **4.7 MHz.** That’s how the **FFT** adds to the capability of the oscilloscope, it provides another point of view for the same data.

**Figure 1. The time domain view in the top grid shows a pulse modulated RF carrier while the frequency domain view in the lower grid shows a uniform distribution of the carrier frequency between 997 MHz and 1002 MHz.
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**FFT**frequency span and resolution bandwidth

In your earliest circuits course, you learned the frequency (frequency domain) of a periodic signal is the reciprocal of the period (time domain). That same relationship appears throughout the

**FFT**setup.

The best place to start with setting up the

**FFT**is choosing the RBW (resolution bandwidth) because it’s related to a single setting. The

**RBW (Δf)**is the incremental step in displaying the FFT frequency axis. In the time domain, the sampling period determines the time between samples. In the frequency domain,

**RBW**is the frequency difference between adjacent “cells” in the spectral view. The R

**B**W is the reciprocal of the time domain record length, also called the capture time as shown in

**Figure 2**. You can control this with the oscilloscope’s horizontal scale or time/division setting. The acquisition duration in

**Fig. 1**is

**20**

**µs.**Thus, the spectrum view’s

**RBW**is the reciprocal of that number, or

**50 kHz.**

**Figure 2. The resolution bandwidth of the frequency spectrum is the reciprocal of the time domain record length, or capture time.**

The next step in the

**FFT**setup is to determine the span of the frequency-domain view—the difference between the highest and lowest frequency in the

**FFT.**Note that

**FFTs**generally start at 0

**Hz**and go out to the span. This is very different from the

**RF**spectrum analyzer, which I’ll explain shortly.

**Read More: FFTs and oscilloscopes: A practical guide**