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When the modulation source is an audio-frequency oscillator and the destination is the Gain of a VCA in the audio signal path, we call the result Amplitude Modulation, or AM for short. I find AM a fascinating topic, not least because it has a quite unexpected result: instead of just sounding like a very fast tremolo, it creates new frequencies that were not present in the original signals! But how does this happen?
Figure 1 [top] and Figure 2 [bottom].Now look at Equation 2. This is identical to Equation 1, except that all the subscripts are the number '2'. This shows that we have a second waveform to consider, and that this has a different maximum amplitude and a different frequency.
Figure 7: [top] The harmonic spectrum of the mixed signals. Figure 8: [bottom] Audio frequency Amplitude Modulation.You'll remember that, in Equation 1, the term a1 determined the maximum amplitude of the wave, and for the sake of argument I will define this as the Gain of the VCA. But we now have a situation where the Gain is being modulated by the instantaneous amplitude of the second signal. So, when the waveform of the Modulator is positive (ie. above the 0V axis) the Gain of the VCA increases, and when it is negative, the Gain of the VCA decreases. But, at every moment in time, we know exactly what the amplitude of the modulating signal is: it's A2, as defined in Equation 2.
Moving on, Figure 10 shows the spectrum of the waveform in Figure 9. Notice that the Modulator has completely disappeared, and that the Sum and Difference signals have half the amplitude of the Modulator (this is what the '1/2's in Equation 6 are telling us).
But before you think that you have grasped this and avoided a headache, don't forget that the second harmonic of the Carrier also interacts with the complete harmonic series of the Modulator, as does the third, the fourth, the fifth... and on and on and on and on! Fortunately, the amplitudes of all but the first few components are very small, so in practical terms you can discount the higher-order series. Nevertheless, it's not hard to imagine that these tones will be very complex. Indeed, they produce superb starting points for complex synthesis using filters and other modulators.
Imagine a single harmonic of a complex waveform lying somewhere just above the cutoff frequency Fc. As you modulate Fc you will find that sometimes the harmonic is attenuated more because of the modulation, while at other times it is attenuated less. In other words, this harmonic is being Amplitude Modulated by the changing action of the filter. Depending upon the width of the modulation (the maximum amplitude a2 of the Modulator) the same is true to a greater or lesser extent for all the other harmonics within the signal. So this time, instead of having one set of harmonics modulating another set of harmonics, we have just a single set, but each component is being modulated in a different way. As I said before, I love this stuff!
The research has reviewed the evidence on the response to amplitude modulation (AM) in relation to wind turbines. It was undertaken by a research team lead by WSP Parsons Brinkerhoff, who are responsible for the overall editorial content of the report, and supported by three independent external reviewers.
The \( y_2\) waveform is acting as a modulator and creates an amplitude envelope. This means its magnitude is determining the magnitude of \( y_1\times2 \). When the value of \( A_2 \) is zero, the modulator has a constant value of 1, and the line \( y_1\times2 \) is exactly equal to \( y_1 \) meaning you will not hear any variation in loudness.
allows us to write the equation for \( y_1\times2 \) as a sum of sine waves, which is equivalent to playing two tones of different frequencies. The fact that rapidly modulating the amplitude of one wave results in a waveform identical to playing two notes of different frequencies is quite remarkable and for more information on such wave int