t)- we just consider a more general way to do this. We can now talk of channels that do two things-add a noise and do a filtering c(t), giving the receiver r(t) = c(t) * s(t) + n(t). We'll also spend some time talking about what goes on at the receiver, which is called equalization. 9.1 Modulators and Pulse Shaping Consider the modulators we talked about in Chapter 5. We talked of ASK, PSK, and QAM (as well as FSK, but we'll leave that one out for now). Look over to the QPSK modulator in Figure 9.1(a) for a refresher. In Figure 9.1(b), we see that in comes m = (10 00 10 10 00), and out goes the waveform s(t). We can express the modulator output, such as this QPSK output, mathematically according to (t)= so(t)+ s,(t)+s2(t)+s3(t)+s4(t) (9.1) (9.2) (9.3) Chapter Nine Acos(Wct+0), iT<t<(i+1)T=Acos(Wct+O)r(t-iT) Acos(Wct + /2), iT<t<(i+1)T=Acos(Wct+/2)r(t-iT) Acos(Wct + TT), iT<t<(i+1)T=Acos(Wct+).r(t-iT) Acos(Wct + 3/2), iT<t<(i+1)T = Acos(wor + 3/2) (t-iT) m=10 00 10 10 00 Accos(Act+1t) Accos(Wct) Accos(Wct+1). Accos(Wct+tc) Accos(Wct) so(t) s1(t) s2(t) s3(t) 54(t) Figure 9.1 Describing a modulator using QPSK as an example (a) input-output relationship (b) input-output example Channel Filtering and Equalizers (9.4) When you write what comes out in this way, it indicates a simple way to build the modulator. For example, the QPSK modulator can be built as shown in Figure 9.2. Here, bits come in and they are mapped by a coder to a complex amplitude indicating the Aee value. This is then passed through what is called the pulse shaper, which turns the information Ajeji, into the shape - Finally, we multiply this by ejwet and take the real part, and, voila, for every two bits that come in we've got coming out. ejwct pulse coder Re {.} shaper Symbol, li=Ajej0; Aej12 m=(10 00) symbols = signals = Figure 9.2 Construction of modulator (e.g. QPSK) Now, examine the modulator shown in Figure 9.3. It is identical in every way to the modulator in Figure 9.2, with one exception. The pulse-shaping filter, which was previously (t), i