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This is referred to as quaternary encoding, and the waveform is shown in Fig. 10.3b. The encoding is symmetrical about the zero axis, the spacing between adjacent levels being 2A. Each level represents a symbol, the duration of which is the symbol period. For the quaternary waveform the
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Figure 10.3 Encoding of 11010010 in (a) binary polar NRZ and (b) quaternary polar NRZ.
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symbol period is seen to be equal to twice the bit period, and the symbol rate is Rsym 1 Tsym (10.2)
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The symbol rate is measured in units of bauds, where 1 Bd is one symbol per second. The periodic time of the squarewave having the greatest symbol repetition frequency is 2Tsym, which is equal to 4Tb, and hence the bandwidth, compared with the basic binary waveform, is halved. The bit rate (as distinct from the symbol rate) remains unchanged, and hence the bandwidth utilization in terms of bits per second per hertz is doubled. In general, a waveform may have M levels (sometimes referred to as an M-ary waveform), where each symbol represents m bits and m The symbol period is therefore Tsym mTb (10.4) log2 M (10.3)
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and the symbol rate in terms of bit rate is Rsym Rb m (10.5)
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For satellite transmission, the encoded message must be modulated onto the microwave carrier. Before examining the modulation process, we describe the way in which speech signals are converted to a digital format through pulse code modulation. 10.3 Pulse Code Modulation In the previous section describing baseband digital signals, the information was assumed to be encoded in one of the digital waveforms shown in Figs. 10.2 and 10.3. Speech and video appear naturally as analog signals, and these must be converted to digital form for transmission over a digital link. In Fig. 10.1 the speech and video analog signals are shown converted to digital form through the use of A/D converters. The particular form of A/D conversion used is known as pulse-code modulation (PCM). Commercially available integrated circuits known as PCM codecs (for coder-decoder) are used to implement PCM. Figure 10.4a shows a block schematic for the Motorola MC145500 series of codecs suitable for speech signals. The analog signal enters at the Tx terminals and passes through a low-pass filter, followed by a highpass filter to remove any 50/60-Hz interference which may appear on the line. The low-pass filter has a cutoff frequency of about 4 kHz, which allows for the filter rolloff above the audio limit of 3400 Hz. As shown in connection with single-sideband systems, a voice channel bandwidth extending from 300 to 3400 Hz is considered satisfactory for speech. Band limiting the audio signal in this way reduces noise. It has another important consequence associated with the analog-to-digital conversion process. The analog signal is digitized by taking samples at periodic intervals. A theorem, known as the sampling theorem, states in part that the sampling frequency must be at least twice the highest frequency in the spectrum of the signal being sampled. With the upper cutoff frequency of the audio filter at 4 kHz, the sampling frequency can be standardized at 8 kHz. The sampled voltage levels are encoded as binary digital numbers in the A/D converter following the high-pass filter. The binary number which is transmitted actually represents a range of voltages, and all samples which fall within this range are encoded as the same number. This process, referred to as quantization, obviously will introduce some distortion (termed quantization noise) into the signal. In a properly designed system, the quantization noise is kept well within acceptable limits. The quantization steps follow a nonlinear law, with
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Figure 10.4 (a) MC145500/01/02/03/05 PCM CODEC/filter monocircuit block diagram. (b) -law encode-decode characteristics. (Courtesy of Motorola, Inc.)
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