In this note we want to examine what happens when a digital oscilloscope has an input with frequency components that are at frequencies at or above the sampling rate of the digital oscilloscope. To help in understanding what happens we are going to ask you to open a simulator in a separate window, and there you will be able to perform some experiments that will help you to understand some of the things that happen in digital storage oscilloscopes. What want you to some some things with a simulator. First, we will describe what happens in the simulator.
First, open the simulator. Click the start button and you should get a display of a signal.
In this first display, you should realize that the number of points in the display is far less than in a typical digital oscilloscope - which is usually in the thousands of points. However, we're trying to show a few things that happen, and we will go with that for now.
Next, change the frequency to 0.5Hz. That gives a period of 2 seconds. Clear the data by clicking the Clear button. Then, click the Start button and observe what happens. You get the same kind of signal but now there are only twenty points in a cycle of the sine wave. Although the points are sparse, the signal is still recognizably a sine wave.
Now, change the frequency to 1 Hz. That has a period of 1 second, and there are now ten points in a sine cycle. Now, things are not timed very well, and you always miss the peak of the sine wave when sampling.
Let's push this even further. Change the frequency to 5 Hz, for a period of .2 sec. Clear the data and generate a new plot. What's that, you say you can't generate a plot? Then try 10 Hz. What do you think the problem is?
Try setting the frequency to 10.1 Hz and observe the results. Those results are particularly interesting because the observed frequency is nowhere near 10.1 Hz. As a matter of fact, it is closer to 0.1 Hz since the sine wave - even though it is decaying - goes through one complete cycle in ten (10) seconds (apparently) for an apparent frequency of 0.1 Hz.. There are things going on there that we discuss in another note on the Nyquist Sampling Theorem. You should realize that the reason that the apparent frequency is 0.1 Hz is that the first sample (at 0.1 seconds) is taken just after a full cycle has elapsed - just as the next cycle is beginning. Then the next sample is taken just a little further into the next cycle.
The problem that we see in the simulations is traceable to the Nyquist Sampling Theorem. The sampling rate (10 samples/second in all of the simulations above with a time interval of 0.1 seconds) has to be twice the highest frequency in the signal. For the signal we have been working with, frequency components are all near the frequency of the sinusoid. (The effect of the decaying exponential envelope is to spread out the frequency components around the frequency of the sinusoid.)
Here, we are more concerned with the effects of the sampling rate on the oscilloscope display, although clearly it is the sampling that causes the effects we want to examine. Let's play a few more games. In the simulator, try a frequency of 2.234 Hz. That produces a signal where the only discernible pattern is in the envelope of the decay. The rest of the display is an almost random scattering of points taken at odd intervals throughout the cycle. That random scattering is referred to as the "Starry Night Phenomenon" for obvious reasons. It looks something like a random smattering of stars in the sky. On a digital oscilloscope with many more points in the trace, there is often less of a discernible pattern in the display.
There is no report for this part. You just need to get checked off by your lab instructor that you did the work.