ne is shown Figure 28.4 Error probability due to Gaussian noise as the solid lines on Figure 28.6. This is seen to have a compact time response in that it always remains within the magnitude of the Nyquist pulse envelope. Thus, at the cost of more bandwidth, tolerance to (small) timing errors is good. The full raised cosine has The steepness of the curve in Figure 28.4 means that small the added feature that the waveform at time T/2 is half the peak changes in signal-to-noise ratio have a significant effect on error amplitude. This leads to good eye shape (see next section), and also probability. Thus digital systems need an adequate design margin to has application to some partial response systems (Bennett and ensure both short and long term reliability. We also see that multi- Davey, 1965). Other pulse shaping strategies which aim to give level systems require much better signal-to-noise ratios. This may good timing tolerance are to be found in (Franks, 1968). be partially compensated by the narrower bandwidth requirements It should be noted that the characteristics of Figure 28.6 imply made possible by a trade-off between the number of transmit levels linear phase properties. Deviations from this condition can lead to and the symbol rate. However for baseband transmission the bal- severe waveform distortion (Sunde, 1961). Equalisers must there- Transmission error performance 28/5 Channel Equaliser Decision circuit Figure 28.5 Waveform shaping for zero intersymbol interference (basic requirement) fore take account of both phase and amplitude. Practical solutions, system to decision timing errors is determined by the rate of closure which can only approximate to the theoretical requirements, aim to of the eye as the sampling time is varied. The height of the eye, at a give acceptably low (but usually not zero) i.s.i. specified decision time, determines the margin over noise. Given distribution probabilities for the noise and timing jitter, it is 28.1.5 The eye diagram then possible to determine the optimum sampl