of modulation index gives an improvement in signal However, in this case, the sideband power is only half the total to noise ratio, as in analogue systems. However, this may be un- 19/8 Digital modulation 0000000000 Figure 19.5 Frequency shift keying: (a) baseband signal; (b) FSK signal; (c) & (d) constituent ASK signals necessary for a digital signal. Moreover, it would reduce the data occupies a bandwidth of approximately 2B. This is twice that throughput obtainable in a given bandwidth. Sunde (1954) obtained needed for ASK. However, if coherent demodulation is used, it is a solution to satisfying Nyquist's minimum bandwidth condition for possible to use a frequency shift of only 0.7B (Clark, 1983). In a the case of FSK. He showed that, with certain assumptions, the multi-level FSK system, a similar separation is needed between the minimum bandwidth is obtained when the frequency shift (f, - f ) frequencies representing each of the levels. Thus, for a given sym- is equal to the data rate in bauds. It is therefore common practice to bol rate, the bandwidth increases with the number of levels. use a frequency shift equal to the digit rate. An FSK signal can be demodulated by a frequency discriminator, If the bandwidth occupied by the sidebands about f 1 and f2 is as described in Chapter 18. Alternatively, a pair of filters tuned to f approximately Bandf2-f,=B, then the spectrum in Figure 19.6(b) and f2 may be used with a pair of envelope demodulators. This is Frequency Frequency Figure 19.6 Spectra for frequency shift keying: (a) large frequency deviation; (b) small frequency deviation Digital modulation of a carrier 19/9 Thus, binary PSK with a phase shift of 180° is identical with binary DSBSC transmission. At the receiver, a coherent demodula- tor with a local carrier cos w t will produce an output signal of +1 and - 1. Since PSK uses DSBSC amplitude modulation, it requires the same bandwidth as ASK and this is less than that needed for FSK. Moreover, since PSK is a suppressed carrier system, all the trans- mi