Specifications

The next plot shows the waveform reconstructions using linear interpolation (i.e., drawing a straight line

between each point):

Figure 20

The "Adequate sampling" samples reproduce the waveform adequately. With some suitable low pass

filtering, this could be an excellent reconstruction of the original waveform. However, the "Inadequate

sampling" reconstruction misses important details in the waveform. With some low pass filtering to

remove the sharp corners, you'd probably conclude the original waveform was about one-third the

frequency of the actual waveform. Other waveform measurements would be in error too.

Exactly this situation can occur when you're using a digital oscilloscope -- and you won't be aware of it

unless you're careful, worry about these things, and look for clues that such things are happening. In

reality, accurate reconstruction of a signal depends on both the sample rate and the interpolation

method used to fill in the spaces between the samples. Some oscilloscopes may let you select either

sin (x)/x interpolation for measuring sinusoidal signals, or linear interpolation for square waves, pulses

and other signal types.

Note a particular behavior in the inadequate sampling reconstruction in Figure 20. If you squint your

eyes at the waveform the connected points make, you might estimate that it was approximately a sine

wave with a period of about 6.5 units on the horizontal axis. This is a behavior called aliasing, where a

signal "appears" that isn't really in the actual signal -- it's an artifact of the sampling, caused by

frequency components in the signal higher than the sampling frequency. If you were using a digital

oscilloscope, the red curve suitably smoothed is what you'd see on the screen and you would be hard-

pressed to know from that picture alone whether what you were looking at was the real waveform or

not. The aliased signal is at a frequency that is the difference between the sampling frequency and the

relevant frequency component in the signal.

Copying/reprinting/republishing without express written consent prohibited.