ly, n = information power/total power (12.14) n-14" (12.15) Chapter Twelve where Px is the power in x(t), and is calculated using the integral For example, if Px=1 and m = 1, then we have a modulation efficiency n = =0.5=50%. 12.2.3 Demodulation of AM Signals-Noise-Free Case In this section, we will study the demodulator used when a modulator sends an AM signal. The demodulator receives the signal r(t) that comes across the channel, and puts out x(t), its best guess on the original information signal x(t). To keep our presentation simple, I'll assume that the input to the demodulator is r(t) = s(t). That is, we will ignore all the channel effects and assume an ideal channel where what comes out is exactly what came in. The idea behind demodulation is simple. Look, for example, at the signal in Figure 12.4(b). Let's say that this signal r(t) = s(t) is coming into the demodulator. The top dotted line in that picture, called the envelope, is simply A (1 + mx(t)) = A (1 + m cosWt). If we can find a way to get that top dotted line out of the received r(t)=s(t), then we in essence have our information x(t). (All we have to do once we get [the top dotted line] A(1 + mx(t)) = A + A mx(t) is subtract A, and multiply the result by the scalar 1/mA.) So the key question in demodulation is: Can we build a simple device to get that top dotted line from the signal in Figure 12.4(b)? The answer is a resounding yes. There are very cheap and simple devices, called envelope detectors, that can easily extract the envelope from the s(t). So, AM receivers are called envelope detectors. An example of an inexpensive envelope detector is shown in Figure 12.6. In this diode figure, the little triangle, a diode, makes all makes all negative values O negative values zero, and leaves all the positive values untouched. For example, with the input of Figure 12.4(a), redrawn in Figure 12.7(a), the output from the diode is Figure 12.7(b). The resistor (R) and the capacitor (C) work together as a low-pass filter. The RC low-pass filter cuts out t