can modulate an analogue carrier by using amplitude modulation, fre- quency modulation, or phase modulation. Some of the basic techniques are described below. Amplitude Shift Keying In Amplitude Shift Keying (ASK) or On-Off Keying (OOK), a binary 1 is represented by the presence of a carrier and a binary 0 is represented by the absence of it. Mathematically, s(t) and Asin(2ft), for binary 1 (2.10) for binary 0 Frequency Shift Keying If a digital signal is used to modulate a carrier in frequency, this is known as Frequency Shift Keying (FSK). Binary FSK is equivalent to applying ASK to two carriers of frequencies, f1 and f2, one being switched on when the baseband signal is 0 and the other when it is 1. Mathematically, binary FSK can be given as for binary 1 (2.11) (Asin(2(fc-k)t), for binary 0 The spacing between the frequencies used for representing bits 0 and 1 (also known as tone distance) is an important parameter in the design of FSK systems. Phase Shift Keying If phase modulation is used to transmit a digital signal, this is known as Phase Shift Keying (PSK). If the signal is binary, the phase of the carrier is shifted between two positions that are 180° apart. Mathematically, binary PSK is represented as Asin(2nft+t), for binary 1 (2.12) for binary 0 PSK signals can have more than two levels. For example, a 4-level PSK signal uses four carrier phases, separated by 90°. PSK is therefore sometimes known as Quadrature Phase Shift Keying (QPSK). To transmit a binary baseband signal, a pair of binary digits is com- bined to form a 4-level signal (00, 01, 10, 11) corresponding to the four phases transmitted. At the receiver, each of the four output values is used to generate two consecutive binary output digits. By this means, the digit rate on the transmission path and the required band- width are halved. Chapter 2 Data Transmission PSK requires a synchronous demodulator, and synchronism is often difficult to main- tain, particularly at high carrier frequencies. The need for accurate carrier recovery can be avo