Measurements
Time-interval measurements
Remember that according to Fourier, a square wave or triangular wave is
made up of a series of sine waves and contains frequencies higher than the
fundamental. If you sample a square wave at a rate equal to four times the
fundamental frequency, then reconstruct the samples as a sine wave, you
have all the information about the square wave, up to that frequency. This is
no different than viewing the same square wave on an oscilloscope with
insufficient bandwidth to reproduce the higher-frequency components. To
accurately reproduce the square wave, you must sample it at a rate at least
twice the highest frequency in its Fourier expansion.
Aliasing
The effect of sampling rate is the same as bandwidth: loss of high frequency
information in the signal. However, there is an additional complication
associated with sampling a signal. If the signal contains frequencies higher
than half the sampling rate, then there will be errors due to aliasing.
Consider sampling a sine wave at a rate less than twice the frequency of the
sine wave as shown in figure 13-25. Notice that the set of resulting samples
is indistinguishable from samples of a lower-frequency sine wave.
Figure 13–25
Sine Wave Having Frequency f and Sampled at Frequency <2f
13–52