the r.m.s. noise for a period of 12 ms or less. This type of noise can be from a number of sources, such as the switching of relays in electromechanical telephone exchanges. Although these "clicks and pops" are annoying to the human ear, data is reasonably tolerant to it. However, impulse noise can cause many serious error rate problems on data or digital circuits. The effects of impulse noise can be alleviated by the use of a wideband clipping circuit followed by a band-limiting filter. This procedure first reduces the amplitudes of the spectral components and then reduces the number of components. Intermodulation noise is due to the presence of the products of intermodulation. If a number of signals of different frequencies are passed through a nonlinear device, a series of second-, third-, and higher-order sum and difference frequencies are produced, which are known as intermodulation products. These components can be inside or outside the frequency band of interest for the device. For most analogue systems with many mul- tiplexed channels, the addition of the very large combination of signals results in an output noise spectrum, which is approximately flat with a frequency across a narrow- band of about 4 kHz. Intermodulation noise differs from thermal noise because it is a function of the signal power at the point of nonlinearity. For a given bitstream, the bit error rate (BER) at the receiver strongly depends on the SNR of the input signal, which is generally expressed in dB. For zero-mean Gaussian noise, the probability of making an erroneous decision is given as (2.17) where a is the voltage difference between the received signal and its associated decision threshold at the decision time and o is the r.m.s. noise voltage. This is the well-known area under the Gaussian tail. The analytical solution to this formula has to be approximated. Figure 2.11 shows an example of a BER graph for a two-level signal under Gaussian noise. Transmission Performance SNR (dB) 2.11 Bit error rate performance in the presence 