because a large amplitude change has only a slight impact on the position of the crossing points. This helps us understand that the noise added to the transmitted signal on the line does not reduce the postdetection S/N as much as in the case of linear modulation. Actually the S/N can be improved in detection. This advantage is paid for by a wider transmission bandwidth. For example, commercial FM broadcasting uses more than 200 kHz of bandwidth for the transmission of a 15-kHz message band. The characteristics of the spectrum of an FM signal are not as simple as those for linear modulation methods. However, in digital FM we use one carrier frequency for each digital symbol value. In the binary case we may transmit 0 for a lower frequency and 1 for the higher frequency, and each Message FM modulator Carrier Frequency modulated carrier wave Spectrum of FM: Frequency/Hz Modulating message Spectrum of the modulated signal, bandwidth >2W Figure 4.6 FM. Transmission transmitted bit generates spectrum similar to the radio-frequency burst shown in Figure 4.2 around its center frequency. Now we see that width of the spectrum also depends here on the data rate, which defines length of the burst in Figure 4.2, and the distance between higher and lower frequencies used. As an example of digital FM, some older generation voice-band modems use the digital form of FM called frequency shift keying (FSK). For example, a 1,200-bps V.23 modem uses two frequencies, 1,300 Hz for binary 0 and the 2,100 Hz for binary 1. Another example is digital frequency modulation of GSM in which two frequencies, 67.7 kHz above and below the nominal carrier frequency, are used for binary transmission [2]. 4.2.4 PM is another method in the class of exponential modulations. In PM the instantaneous phase, instead of frequency, is varied linearly according to the message. Therefore, if the message has discontinuities, there will be disconti- nuities in the modulated carrier wave as well (Figure 4.7). The spectral char- acteristics are nearly the same a