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Regarding an AM-DSB modulator fed by a sine wave modulating signal wm and carrier frequency wc:
In the frequency domain: the spectrum is made up by three lines: one centered in wc, one centered in wc+wm and other centered in wc-wm
In time domain: The amplitude of the carrier will be changing according to the instantaneous value of wm. If the amplitude of wm is equal to the amplitude of wm, the modulated signal's amplitude will be changing from 0 and 2 x amplitude of wm (or wc). In this case the AM coefficient index is 100%. If you disconnect the modulating signal, the output of the modulator will be the a sine wave in wm.
Regarding an AM-DSB-SC modulator fed by a sine wave modulating signal wm and carrier frequency wc:
In the frequency domain: the spectrum is made up two lines: one centered in wc+wm and other centered in wc-wm. The carier is suppressed.
In time domain the modulated signal will be changing from 0 to the amplitude of wc. There is no definition of modulation index. If you turn off the modulating frequency, the modulator's output will be zero.
Now the most important characteristic of the AM-DSB-SC, is that the phase of the modulated signal jumps 180 deg. each time the modulating signal inverts its polariity.
By the way due to this characteristic AM-DSB-SC are the kind of modulator used to generate digital modulation in BPSK and QPSK.
Amplitude modulation can be done in a number of ways...one among them is DSB Sc , the difference lies in two points :
1. Number of Sideband
2. Carrier signal.
In AM there can be either one or two sideband but the carrier signal is always sent with the modulated signal.
Whereas DSB has two sidebands and the carrier is suppressed.
What this implies is there would be no carrier signal with the modulated signal,this would have several implications on Bandwdth.
DSB Sc is considered superior to AM due to its lesser BW requirement and better S/N ratio (for proper design ).
Refer to Analog and Digital Communication Techniques by Couch for more details.
electron_boy is correct...but sometimes the carrier is not completely removed. Its power is reduced relative to the sidebands. This is to facilitate "synchronous demodulation" in RXCVRs where a phase locked loop mechanism is used to "lock" and generate an in-phase LO signal and then this LO and the DSB-SC AM signal are both fed into a mixer to downconvert and hence perform demodulation to recover the transmitted baseband signal.