Amplitude modulation is defined as the multiplication of one time-domain signal by another time-domain signal. The signals may or may not be complex in nature, i.e., either or both signals may contain harmonics components. It is impossible to have amplitude modulation unless at least two different signals are involved. The signals may be electrical in nature, or they can be vibration signals. Modulation is inherently a non-linear process, and always gives rise to frequency components that did not exist in either of the two original signals

The figure below shows a simple amplitude modulated sine wave that was generated by a low-frequency sine wave being multiplied by a higher-frequency sine wave. The low frequency sine wave is called the modulating frequency. It can be seen riding along as the envelope of the higher frequency, or "carrier" signal. Simply put, an amplitude-modulated carrier is a signal that has been caused to vary in amplitude by multiplication by another, lower-frequency signal.

Amplitude Modulated Wave Form

If the amplitude-modulated signal shown here is passed through a frequency analyzer, the following spectrum is the result. The highest peak is the carrier frequency. The right-hand peak is the “upper sideband”, and has a frequency of the carrier frequency plus the modulating frequency. The left-hand peak or “lower sideband” has a frequency of the carrier minus the modulating frequency. The sidebands are sometimes called “sum and difference” frequencies because of their symmetrical spacing around the carrier.

Amplitude modulation also occurs in sound reproducing equipment, where it is called Intermodulation Distortion. The sum and difference frequencies are not in musical harmony with the tones that cause them, making intermodulation a particularly noticeable form of sound distortion.  

Spectrum of Modulated Wave Form

It is a fact of amplitude modulation that all the information in the modulated signal resides in the sidebands, and none is contained in the carrier. This is the reason that vibration analysts pay so much attention to sidebands in machine vibration spectra -- much information about the machine problems is concentrated there.

Amplitude demodulation is defined as the recovery of modulation information contained in an amplitude modulated carrier. It is performed simply by full-wave rectification of the modulated waveform. This just turns all the negative-going peaks into positive-going peaks, effectively doubling the frequency of the carrier. 

Rectified Wave Form

The modulating waveform is easily seen as the envelope of the rectified signal. To recover the modulating signal, you simply pass the rectified carrier through a low-pass filter to remove the high-frequency fluctuations due to the carrier. 

Recovered Modulating Signal

This process of demodulation is exactly what happens in an AM radio - the carrier is a very high frequency signal generated by the radio station, and the modulating signal is the voice or music that constitutes the program. The radio receives the modulated carrier, amplifies it, and rectifies (“detects”) it to recover the program.

Tip from  Introduction to Machine Vibration by Glenn D. White

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