Sample Rate

The SAMPLING THEOREM states that for a baseband signal to be faithfully reproduced in sampled form, the sample rate must be greater than twice the highest frequency present in the signal.

fs > 2 BW

where

fs = sample rate
BW = bandwidth of the signal

The minimum sample rate is known as the NYQUIST RATE. This relationship guarantees that slightly more than two samples per cycle are acquired on a sine wave having a frequency right at the bandwidth limit. This equation defines the minimum theoretical sample rate. In practice, a higher sample rate is required to represent the signal accurately.

The sample rate and bandwidth specifications on a digital scope tend to be confused. Does a 100-MHz digital scope have a sample rate of 100 MHz or a bandwidth of 100 MHz? To help alleviate this problem, digital scope manufacturers have settled on specifying the sample rate in samples per second and the bandwidth in hertz. More typically, the sample rate is in megasamples per second (MSa/sec) and the bandwidth is in megahertz (MHz).

Example 4-2.
What is the minimum sample rate required by the sampling theorem to represent completely a signal having a 100-MHz bandwidth?
The sampling theorem requires

fs > 2 BW
fs > 2 X 100 MHz = 200 MSa/sec

The sample rate fs must be greater than 200 MSa/sec.

This still leaves the user with the question of how do sample rate and bandwidth relate in a practical digital scope? Or how much sample rate is required for a particular bandwidth? As we shall see, the answer depends on the sampling technique used in the oscilloscope.

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