The amount of information and the speed at which it is transmitted determines the base bandwidth occupied by a signal. For analogue signals, the base bandwidth is the range of frequencies contained in the signal; it is not the same as that occupied by a radio frequency carrier modulated by the signal. Examples of base bandwidths are given in Table 8.1.
Table 8.1 Base bandwidthsSpeech
High fidelity reproduction 15–15 000 Good fidelity 150–7000
Public address 200–5000
Restricted bass and treble 500–4000
Toll quality (good quality 300–3400
Communications quality (radio 300–3000
communication)
Mobile radio 300–2700
(12.5 kHz channel separation)
Music (for FM broadcasting) 30–15 000 Video 60Hz–4.2MHz
Bit rate (b/s) and baud rate are terms used to specify the speed of transmitting digital information. Where the duration of all the signalling elements is identical the terms are synonymous, but not where the duration of the information bits differs.
As the term implies, the bit rate is the number of bits transmitted per second but the baud rate (after J.M.E. Baudot, the code’s inventor) is the reciprocal of the length, in seconds, of the shortest duration signalling element. Figure 8.1(a) shows a binary code pattern where
110Time
10101 Symbol periods
Bit rate = 1000 b/s = 1000 baud
Letter ‘J’ CCITT-2 code Average bit rate = 1/0.23 = 43.5 b/s Baud rate = 1/0.0 22 = 45.5 (b)
Figure 8.1 Bit rate and baud rateall the bits are of equal duration, in this case 1 millisecond; the bit rate is 1000 per second and the baud rate is 1/0.001 = 1000 also.
On telegraphy systems all the bits may not be of the same duration and Figure 8.1(b) shows the pattern for the letter ‘J’ in the CCITT2 code as used for teletype. In this code a letter is composed of 5 elements, each of 22 ms duration, but each letter is preceded by a space of 22 ms and followed by a mark of 31 ms. The duration of each character is 163 ms – the time for 7.5 elements – but is comprised of only 7 bits.
The baud rate is 1 /0.022 = 45.5baud.
The average bit duration is 163/7 = 23.29 ms. The average bit rate is 1/0.023 = 43.5 bits per second.
A stream of binary coded information is composed of pulses where, say, a pulse (mark) represents digit 1 and the absence of a pulse (space) represents digit 0. The highest frequency contained in the information is determined by the bit – or baud – rate. Because a series of 1s or 0s may be consecutive in the data stream, the pulse repetition rate will vary throughout the message although the bit rate will be constant, and over a long period of time as many spaces will be sent as pulses. Transmitting either a stream of spaces or of marks requires no bandwidth; it is only when a change of state occurs that frequencies are produced. In the duration of one cycle (Figure 8.1(a)) two bits may be carried and the maximum fundamental frequency contained in the wave is one-half the number of bits per second, i.e. the channel capacity, bits/second, equals twice the bandwidth in hertz.
C = 2δf log2N
where
C = channel capacity, bits per second
δf = channel bandwidth, Hz
N = number of coding levels (2 in binary system)
C = δf log2(1+S/N)
where S/N = the ratio of total signal power to total noise power at the receiver input within the bandwidth, δf.