own in Figure 12.9(d). You can clearly see, comparing the envelope of Figure 12.9(d) with the x(t) of Figure 12.9(a), that these have completely different shapes. In fact, in this case, the envelope of s(t) is |x(t)| and not x(t). So, the envelope detector does not work for the DSB-SC signal. This is unfortunate, because envelope detectors are SO inexpensive. Nevertheless, some designers did decide to use DSB-SC. But first, they had to come up with a demodulator at the receiver side, to get x(t), given r(t). The demodula- tor that they found worked well is shown in Figure 12.10. The input coming into the demodulator is (12.20) This gets multiplied by a cosine term, leading to Analog Communications -fc+fm fc-fm fc+fm Figure 12.8 DSB-SC (a) Information signal in frequency domain, X(f) (b) Sent signal in frequency domain, s(f) (12.21) (12.22) Next, this signal is passed through a low-pass filter, which cuts out the high- frequency term, leading to the output (12.23) Finally, a multiplication is applied to generate x(t). This demodulator is a little more complex than that of AM. DSB-SC gives you a choice-spend less power in transmission by using DSB-SC, or use a less expensive receiver by using AM. Chapter Twelve x(t) = cosWt x(t) = cosWt AccosWct s(t) = s(t) = x(t) . AccosWct = AccosWt cosact envelope of s(t) Figure 12.9 (a) Information signal x(t) = cosWt (b) Creating sent signal s(t) (c) Sent signal s(t) (d) Envelope of s(t) Analog Communications r(t) = s(t) r'(t) r"(t) = (Acx(t)cos(w)t) cos(Wct) Figure 12.10 Demodulator for DSB-SC Given r(t) = s(t), it outputs x(t) Example 12.2 Assuming A = 4: (a) Determine the output (in time) of the DSB-SC modulator when the input corresponds to Figure E12.3. (b) Determine the output (in frequency) of the DSB-SC modulator when the input corresponds to Figure E12.4. Figure E12.3 The input to DSB-SC modulator for (a) Figure E12.4 The input to DSB-SC modulator for (b) -100Hz 100Hz Solution: (a) The output signal corresponds to S (t)=4x(t) cos wct (E12.2) Chapter Twelve In Figure E