ier wave Figure 4.3 CW modulation. Introduction to Telecommunications Network Engineering peak value of the carrier varies in accordance with the instantaneous value of the modulating signal and the outline wave shape, or envelope, of the modu- lated wave follows the shape of the original modulating signal as shown in Figure 4.4. Thus, the unique property of AM is that the envelope of the modulated carrier has the same shape as the message. We can show with the help of a simple mathematical analysis that when a sinusoidal wave at carrier frequency fc Hz is amplitude modulated by a sinusoidal modulating signal at message frequency fm Hz, the modulated wave contains the following three frequencies, as shown in Figure 4.4: The original carrier frequency, fc Hz; The sum of the carrier and modulating signal frequencies, (fc + fm) The difference between the carrier and modulating signal frequencies, (fc fm) Hz. These sum and difference frequencies are new, produced by the AM process and they are called sideband frequencies. In this case the bandwidth of the modulated signal is Envelope Message AM modulator Amplitude modulated Carrier wave Time/sec carrier wave Spectrum of AM: Carrier Upper Lower sideband sideband f-W fcf fc fc+fm fcW Frequency/Hz Spectrum of the modulating message Spectrum of the modulated signal Figure 4.4 Amplitude modulation and its spectrum. Transmission (4.1) If the modulating signal contains multiple frequency components, a band of frequencies such as those in speech or music, the AM process trans- fers the message spectrum with the carrier. The message spectrum appears after the modulation on both sides of the carrier and the required bandwidth is doubled. Figure 4.4 shows an example in which the original message with baseband bandwidth W modulates a carrier at the frequency fc Each individ- ual frequency component that the message contains produces upper and lower sideband frequencies around the carrier frequency, and complete upper and lower sidebands that contain all frequencies of the messag