 |
| Figure 1. A 100 MHz sine wave in the time domain and its spectrum in the frequency domain showing the one peak at 100 MHz. Click on any image to enlarge. |
Teledyne LeCroy Fellow
The following piece was published in Signal Integrity Journal and is excerpted here by permission of Signal Integrity Journal.
***************************
We live in the time domain. This is where we measure all digital performance. But sometimes, we can get to an answer faster by taking a detour through the frequency domain. With these six principles, we can understand how an oscilloscope transforms time domain measurements into a frequency domain view. All six principles are applied “under the hood” by oscilloscopes with a built-in FFT function. (Our note: Also by software packages designed for spectral analysis, such as the SPECTRUM-1 and SPECTRUM-PRO-2R options.)
1. The spectrum is a combination of sine wave components
In the frequency domain, the only waveforms we are allowed to consider are sine waves. There are other special waveforms combinations of which can describe any time-domain waveform, such as Legendre polynomials, Hermite polynomials or even wavelets. The reason we single out sine waves for a frequency domain description, is that sine waves are solutions to second order, linear, differential equations—the equations found so often in electrical circuits involving resistor, capacitor and inductor elements. This means signals that arise or have interacted with RLC circuits are described more simply when using combinations of sine waves than any other function because sine waves naturally occur.
