Time Waveform Analysis

Problem 1

Is the waveform below amplitude modulation or beating?

Assuming it is amplitude modulation, please draw or describe the spectrum you will see is a specific

way - in other words, calculate the applicable frequencies.

Next assume it is beating. What are the frequencies? What will the spectrum look like? What is the

relative amplitude of the two frequencies?

It is difficult to tell from the time waveform alone if this is modulation or beating. If we knew the forcing frequencies of what was being monitored we could perhaps tell which it is, but without that information we cannot.

Answer

If this is amplitude modulation, the center frequency or frequency being modulated has a period of 0.01. The frequency is FHz = 1/Ps = 1/0.01 = 100 Hz.

Next count how many cycles are in one cycle of modulation. There appear to be 20, giving us a period of modulation of 0.2 sec.The modulating frequency is therefore F = 1/0.2 = 5 Hz. Therefore a 100 Hz wave is being modulated at a rate of 5 Hz. The spectrum will have a peak at 100 Hz with 5 Hz sidebands or 95 Hz, 100 Hz and 105 Hz.

If this is beating, one of the frequencies is 100 Hz, as calculated above. The beat period is 0.2 sec, making the beat frequency = 1/0.2 = 5 Hz. 100 Hz is the average frequency. The two beating frequencies are 100 + 2.5 and 100 - 2.5 Hz. In the spectrum we will simply see two peaks, one at 97.5 Hz and one at 102.5 Hz. The two peaks will be close to the same amplitude because when they are out of phase and subtract, the waveform is at a minimum which is close to a value of zero.

Student question

Where did 2.5 come from, how was it calculated?

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