rrespond to 2 bps. If we use a sinc pulse as in Figure 4.13, the preceding and following pulses do not influence the detection of a transmitted pulse, because each received pulse is measured at a zero crossing point n 1/(2W) of the other pulses. We may increase the number of peak values of sinc pulses from two to four, from four to eight, for example, in order to increase the bit rate while keeping the symbol rate unchanged. Figure 4.14 shows a simple example where symbols are rectangular pulses with four symbol values and each sym- bol carries two bits (k = 2) of information. Generally, the bit rate depends on modulation rate according to rb=k.r.bps (4.9) Transmission where k represents the number of bits encoded into each symbol. Then the number of symbol values is M = 2k and the bit rate is given as rb= bps. In the example of Figure 4.14, the number of symbol values is M = 2k = = 4, and the bit rate Vb = k r bps = 2r bps. Then the symbol rate of 1 kbaud makes the bit rate 2 Kbps. The unit of symbol rate, sometimes called the modulation rate, is bauds (symbols per second). Note that the transmission rate in bauds may represent a much higher transmission rate in bits per second. Table 4.1 shows how the bit rate of a system depends on the number of symbol values. Figure 4.14 also shows a data sequence of sinc pulses with four ampli- tude values. The required bandwidth for pulses in this sequence is the mini- mum bandwidth B = r/2 = 1/(2T) according to (4.8) and Figure 4.13. When pulses are detected by sampling as shown in Figure 4.14 each pulse can be detected independently because values of all other pulses are equal to zero. In the preceding examples, the amplitudes of the pulses contain the information. This is the principle of PAM, as discussed earlier. This is not the only alternative. We can use other characteristics of the signal as well to create multiple symbol values, for example, the phase of a carrier, as we did in the case of QPSK and 8-PSK in Figures 4.8 and 4.9. There we used a certain modulation r