Examples on AM Communication and Fourier Series

Example on AM communication system:

In the applet, press CLEAR to clear the buffer first, using the following parameters to create a function: sign=+, amplitude=5, frequency=1, waveform=sine, power=1. The function is 5*Cos(2*pi * 20). To see the plot of this function, press "+". Then the applet adds 5*Cos(2*pi * 20) to zero and stored the result in the buffer, i.e. the buffer becomes 5*Cos(2*pi * 20). Now you should see a 20-cycle cosine on the Screen panel. The maximum and the minimum amplitudes should be labeled 5 and -5 respectively on the top portion of the Screen panel. Save the funcition as the message. Clear the buffer. Then choose another function as the carrier with these parameters: sign=+, amplitude=5, frequency=100, waveform=Cosine and power=1. Now the message and the carrier are set. Press Encode. The screen will display the waveform shown in figure 1c. Go to Filter panel and change the values to amplitude=0.1, bandwidth=50, frequency=0, and type=lowpass. Press Decode, and you will see the screen displaying a wave that is very similar to the 5 * Cos(2*pi*20). The only difference between the original message and the recovered message is that the recovered message gets a gain on amplitude and some delays in time through the filtering.


fig.1a - the message


fig.1b - the carrier signal

fig.1c - the transmitted signal

fig.1d - the recovered signal


Example on Fourier Series

First clear the buffer, and then add 5 Cos(2*pi *10), 5 Cos(2*pi *30), and 5 Cos(2*pi*50). When you finish, you should see a waveform as shown in figure 2a. I call the waveform in Figure 2a SUM. The objective of this example is to extract each of component out of SUM. SUM should contain the sinusoidal components at 10Hz, 30Hz, and 50Hz. We are going to extract the components, so follow the steps

  1. Save SUM as message. Doing that we do not need to reconstruct SUM later on when we need it again.
  2. In Filter panel, set amplitude to 0.1, bandwidth to 10, and frequency to 10hz.
  3. Press Filter. The screen should display a 10 hz component with gain in amplitude as shown in figure 3a.
  4. Now try to extract the 30hz and 50 hz components. Then press M. The screen should display SUM, and the default value is set to the SUM. Replace the value of the filter frequency to the frequency of the component you want. Press Filter. The results should look like figure 3b and 3c.
  5. After that, let's try to filter at 20 hz. What result do you expect? The result is shown in fig.3d.


[ figure 2a - sum of 3 cosines]

[ figure 3a - 10 hz component]


[ figure 3b - 30 hz component]



[ figure 3c - 50 hz component]


[ figure 3d - a non-existent component at 20hz.]

For more information and examples about AM communication system, please see my partner's web pages at http://heppc.phys.hawaii.edu