pander This means that the bandlimited signal can be represented by a is called a compander. sequence of samples as in Equation 4.74 sampled at the rate given There are basically two types of compander in current use, u-law by Equation 4.75 the SO called Nyquist rate. These samples may then and A-law. be encoded using various techniques giving a digital representation The transfer characteristic of the compressor is represented by a of the analog signal. memoryless nonlinearity c(x), where X is the sample value of a random variable X denoting the compressor input. In the u-law x.=x(2w) (4.74) compander, c(x) is continuous, approximating a linear dependence on X for low input levels and a logarithmic one for high input levels, as in Equation 4.79 for fs=2W samples per second (4.75) One such technique is Pulse Code Modulation (PCM), the essen- (4.79) tial operations being sampling, quantising and encoding, usually performed in the same circuit, called an analog-to-digital converter (ADC). It should be noted that PCM is not modulation in the conventional sense of the word, since modulation usually refers to the variation of some characteristic of the carrier wave in accord- The special case of uniform quantisation corresponds to the case ance with an information bearing signal. The only part of PCM that where u = 0. The u-law is used for PCM telephone systems in the is similar to this definition, is sampling. The subsequent use of USA, Canada and Japan. quantisation, which is basic to PCM, introduces a signal distortion In A-law companding, the compressor characteristic is piecewise, that has no counterpart in conventional modulation. made up of a linear segment for low-level inputs and a logarithmic Let x(t) denote a sample function emitted by a source, and let segment for high-level inputs. This type of compander is used for represent the samples taken at a sampling rate greater than the the PCM telephone systems in Europe. Nyquist rate, 2W, where W is the highest frequency present in the In PCM each sample of the