This slide illustrates the use of real time sampling. The waveform at the top is a very narrow sinusoidal signal. The Nyquist theorem specifies sampling this at a minimum of 2x the frequency of interest. In this example it can be seen that the sine wave is sampled with five sample points and then the reconstructed wave form is shown on the screen. Pulse and square wave type wave forms are very broadband, and are extremely rich in harmonics. These must be sampled typically ten times. The lower illustration shows that when dealing with pulses and square waves more sampling points are required to reconstruct the wave form. This is where the digital bandwidth of the scope comes into play, offering enough memory and a high enough sampling rate to capture the true shape of the signal.