he rapid variations in the signal and leaves the slow variations intact. That is, for the input of Figure 12.7(b), it creates an output of approximately that shown in Figure 12.7(c). Given the incoming s(t), we've got its enve- Low-Pass Filter lope pulled out, which means-good Figure 12.6 An implementation of an AM news-we've pretty much got our x(t). demodulator = envelope detector Analog Communications Ac(1 + mx(t)) r(t) = s(t) cos(Wct) output of Ac(1 + mx(t)) low-frequency term diode cos(Wct) high-frequency term output of Ac(1 + mx(t)) RC LPF Figure 12.7 Workings of envelope detector of Figure 12.6 (a) input (b) diode output (c) LPF output 330 Chapter Twelve 12.2.4 An Alternative to AM-DSB-SC Some use an alternative to AM called double sideband suppressed carrier, which merci- fully is written and spoken in shorthand using the acronym DSB-SC. In AM, we sent (12.16) In DSB-SC, we send pretty much the same thing, only we get rid of the "1" and the "m"; that is, in DSB-SC, we send s(t)=A,x(1)cosw,t (12.17) In some ways this is a good thing, and in some ways it isn't. To see its benefits, let's look at the frequency domain, and study the Fourier transform of the DSB-SC sent signal s(t)-that is, study S(f). Using simple Fourier transform properties, and the s(t) of Equation (12.17), we find (12.18) (12.19) So, if X(f) looks the way it's drawn in Figure 12.8(a), then it follows that S(f) looks like Figure 12.8(b). We can see that in DSB-SC, we are not wasting any power sending an impulse at WC (as in AM, which wastes power here, as shown in Figure 12.5). But, alas, it was not all good news for DSB-SC. People said: Well, we need a de- modulator for it-let's try to use the envelope detector. Let's say x(t) = cos (Wt) (where W is very small) as shown in Figure 12.9(a). That means that s(t) = A cos (Wt) cos(wt), which corresponds to the multiplication shown in Figure 12.9(b) and leads to s(t) = A cos (Wt) s(wt) as shown in Figure 12.9(c). Now, let's look at the envelope of s(t), which is the dotted line on top of it, sh