**Uncertainty Principle**

**What it shows:**

A pulse-modulated electromagnetic signal is simultaneously displayed in the time domain (on an oscilloscope) and in the frequency domain (on a spectrum analyzer). Using ∆n for the frequency spread (uncertainty in frequency) and ∆t for the duration of the pulse (uncertainty in the time domain), the frequency-time uncertainty relation is given by ^{1}

∆n ∆t ≥ ^{1}/_{4π}

By progressively shortening the length of time that the carrier signal is on, the inverse relation between pulse length and spectral-energy...