ained when the carrier at the transmitter is switched on at shape, so is the impulse response of the filter. The (sin x)/x pulse has a uniform spectrum up to frequency W, so the matched filter is an arbitrary instants. Consequently, the carrier must be synchronised ideal low pass filter with cut off frequency W. This is hardly with the baseband signal and be an exact multiple of its digit rate. surprising, since it passes all the energy of the pulse and stops all If this is not possible, an envelope demodulator should be used to noise outside the band of the signal. In the case of a sinusoidal remove the effect of carrier phase variation. Use of a matched filter carrier which is amplitude modulated by a (sin x)/x pulse, the only improves the signal/noise ratio by about 1dB, SO the difference matched filter will be an ideal band pass filter of bandwidth 2W, between the input signal/noise ratios required for coherent and centred on the carrier frequency. non-coherent ASK is only about 1dB (Bylanski and Ingram, 1980). In a digital communication system, the input to the receiver It can be shown (Peebles, 1976) that the bit error probability for a should be band limited by a well designed filter. Consequently, the binary non-coherent ASK system is approximately given by Equa- tion 19.36. improvement obtained by using a matched filter or correlation detector is likely to be only about 1dB (Brown and Glazier, 1974). (19.36) 19.3 Digital modulation of a carrier Single sideband suppressed carrier (SSBSC) transmission is un- suitable for digital data, because the baseband signal has a substan- 19.3.1 Amplitude shift keying tial low frequency content. Vestigial sideband (VSB) transmission (see Chapter 18) can be used. It enables a significant bandwidth If a binary signal is used to modulate the amplitude of a carrier to saving to be obtained at high data rates (Bennett and Davey, 1965). the greatest possible depth, the carrier is switched on and off. This For example, 9600 baud transmission can be obtained over tele- is kno