y in time, its frequency content or spectrum extends over a wide frequency range and we say that the signal has a wide bandwidth. Transmission Figure 4.13 shows the shape of a rectangular pulse with duration T before and after it passed through an ideal lowpass channel of bandwidth B. For example, if the duration of the pulse T=1 ms, distorted pulses are shown in the figure for the channel with bandwidths B = 2.1/T=2 kHz, B = 1/T = 1 kHz, B = 1/2 . 1/7 = 500 Hz, and B = 250 Hz. If the next pulse is sent immediately after the one in the figure, the detection of the pulse value will be impossible if the bandwidth is too narrow. The spread of pulses over other pulses, which disturbs detection of other pulses in the sequence, is called intersymbol interference. In baseband transmission, a digital signal with r symbols per second, bauds, requires the transmission bandwidth B to be in hertz: B>r/2 (4.8) Thus the available bandwidth in hertz determines the maximum sym- bol rate in bauds. Note that the symbol is not necessarily the same as the bit, but it can carry a set of bits if it is allowed to get many different values. We can find the theoretical maximum of the symbol or baud rate with the help of a special pulse called the sinc pulse. The shape of the sinc pulse is drawn in Figure 4.13 and it has zero crossings at regular intervals 1/(2W). With the help of Fourier analysis, we can show that this kind of pulse has no spectral components at frequencies higher than W. If the channel is an ideal Pulse distortion in Rectangular B=2*1/T Distorted pulses a lowpass channel: input pulse at the output of the B=1*1/1 channel. The shape :=1/2*1/T of the output pulse Transmission depends on the channel, B = 1/4* 1/ bandwidth B bandwidth B of the channel. Sinc-pulse and the minimum transmission bandwidth: The sinc-pulse: Next pulse Spectrum of the Ideal lowpass channel with sinc-pulse bandwidth B 1/(2W) Time/sec 3/(2W) Frequency/Hz 2/(2 W) For a baseband digital signal with rsymbols per second, the bandwidth must be B > = r/2. 