The Fast Fourier Transform (FFT) math function is an invaluable feature found in most high-performance benchtop digital oscilloscopes, including all ZTEC modular oscilloscopes. The FFT function converts an acquired time-domain waveform into its frequency components, providing insight into how a waveform behaves in the frequency domain.

FFTs are used in a number of applications. Key uses of the FFT function include finding the frequency of noise and interference signals, identifying the harmonic content and distortion of a waveform, and testing the frequency response of filters.

FFT calculations are part of a long list of standard calculations included on all ZTEC M-Class and C-Class oscilloscopes. ZTEC oscilloscopes provide excellent frequency-domain accuracy by performing FFT calculations on waveforms up to 524,288 time-domain samples. FFT data can be displayed in linear magnitude, log magnitude, phase, real, or imaginary components on M-Class instruments.

Additionally, ZTEC oscilloscopes give users the ability to optimize their frequency-domain measurements by offering FFT windowing. Four windows (Hanning, Hamming, Rectangular, and Blackman) are available on all ZTEC M-Class and C-Class oscilloscopes. A fifth window (Flat Top) is available on M-Class oscillocopes only. For more information about selecting the right FFT window, based on the time-domain signal you are analyzing, please read our Knowledgebase article on FFT windowing.

Sine wave

The FFT of an ideal sine wave consists of a single spike in the frequency domain. The screen images below show the time domain and frequency domain traces of a 100 kHz sine wave. Notice that you see only one main spike at 100 kHz (The horizontal scale on the FFT plot is 125 kHz/div).

Square wave

The FFT of an ideal square wave has diminishing odd harmonics extending to infinity along the frequency axis. In these screen images of a square wave and its FFT, you can see the main spike of the fundamental frequency (100 kHz) followed at regular intervals by the odd harmonics (3rd, 5th, 7th, etc.). Notice that you also see lower magnitude even harmonics in the FFT plot which indicates that this is not a perfect square wave.

Triangle Wave

As with ideal square waves, ideal triangle waves consist only of odd harmonics. A key difference between the square wave and the triangle wave is how quickly the high-order harmonics roll off. The triangle wave harmonics shown in the FFT plot below roll off more quickly than the harmonics of the square wave shown above. In the square wave FFT, you can still clearly see the 11th order harmonic. In the triangle wave FFT, harmonics above the 3rd order are barely visible.

Ramp/Sawtooth Wave

Unlike the square and triangle waves discussed above, ramp or sawtooth waves consist of both even and odd harmonics. Notice the magnitude of the 2nd and 4th order harmonics seen in the FFT plot below.

DC Wave

A DC wave is simply a signal that maintains a constant level. As such, an FFT of a DC wave is simply a single spike at DC. Notice the orange spike on the very left edge of the FFT plot below.

Noise

Pure noise consists of random signal variations and contains no repeating components. Noise in the time domain also appears as noise in the frequency domain (FFT).

FM Wave

Our final example shows an FM (frequency modulated) waveform. An FM waveform delivers information by varying the frequency of the signal. In this example, the carrier frequency is 100 kHz and the modulation frequency is 50 kHz. In other words, the frequency of the FM signal will vary between 50 kHz and 150 kHz. The FFT of the FM signal shows a major peak representing the carrier frequency at 100 kHz (50 kHz/div horizontal scale) and also much shorter peaks at 50 and 150 kHz. The 50 kHz and 150 kHz signals are referred to as sidebands.

• What is Fast Fourier Transform?
• LabVIEW FFT example using ZTEC’s M-Class oscilloscope
• FFT windowing for ZTEC oscilloscopes
• Frequency Domain Waveform Measurements: SNR, THD, SFDR SINAD, ENOB, and more