# What is Amplitude Modulation?

When two sinusoidal waveforms of different frequency are added together then because the peak and troughs positions of the two waveforms do not coincide 'wave interference' occurs. This produces a resultant waveform with differing amplitude, frequency, and envelope to the original waveforms. These effects are easily seen by adding two sine waves together, each having the same steady amplitude but differing slightly in frequency. Figure 1 shows an example waveform of such a summation using sine waves of 399 and 401Hz.

### Figure 1: AM Waveform

As can be seen the 'beating' effect on the envelope of the resultant waveform is both distinct and regular. Since the two signals are sinusoidal the resultant waveform can be predicted using the following mathematical formula:

The two source waveforms, x1 and x2 are: x1 = a sin(1t) x2 = a sin(2t)

With the resultant waveform represented as:

x = x1 + x2 = a sin(1t) + a sin(2t)

= 2a sin[0.5(1t + 2t)] cos[0.5(1t - 2t)]

This formula allows us to extract two important variables of the new resultant waveform, the frequency of envelope beating (0.5(1t - 2t)), and its frequency (0.5(1t + 2t)). As can be seen, the envelope beating frequency is simply the difference between the frequencies of the two waveforms, and the frequency of the new waveform is the average of the two waveforms. Therefore if we take our previous example, the resultant waveform has a frequency of 400Hz, and the frequency of the envelope beating is 2Hz.

It is this envelope beating that can be termed as Amplitude Modulation, the modulation of a 'signal' onto a 'carrier' waveform, in the previous example the 400Hz carrier (average of the two component sine waves) has in effect been Amplitude Modulated with a 2Hz (the difference of the component sine waves) signal. This signal is said to have a 'modulation depth' of 1, meaning that the ratios of the signal and carrier amplitudes are equal (as were the summed waveforms), making the amplitude of the envelope trough 0. However, if the component waveforms are not of equal amplitude then one will become dominant upon the other changing the frequency, envelope, and 'modulation depth' of the resulant signal. These are the effects which will be examined in the next section ' Single Channel AM Experiments ', examining the effects of combined sine waves in a single filter bank channel.

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