ctrum in the fre- quency domain. In other words, the spectrum of the sampled pulse is shaped by the spectrum of the sampling waveform. In most cases the sampling waveform consists of narrow, square (flat- topped) pulses. This means that the power spectrum of the sampling waveform, P(f), is a sinc function, which implies an attenuation of the high-frequency component of the message signal. This phenomenon is referred to as the aperture effect and can be compensated for by employing equalizers at the receiver. Chapter 1 Voice Transmission Quantization Quantization is a process in which the amplitude of the sampled pulses is approximated to discrete values. The quantization is referred to as uniform if all quantization steps have an equal length. The error of approximation in the quantization process is called quantization error. If the quantization noise level is donated by e, then the quantization noise power can be given by (1.12) where P(e) is the probability density function of e. Because the quantization error is distrib- uted uniformly during each quantization level, the P(e) can be written as (1/8 -8/2<e<8/2 (1.13) otherwise where 8 is the quantization step size. Therefore, equation 1.12 can be written as (1.14) Equation 1.14 shows that the quantization noise depends only on the quantization step size. Evidently, the smaller quantization step size results in a lower quantization noise value but requires more bits for coding. If quantization is realized by using N bits, the maximum signal-to-noise ratio (SNR) can be written as (1.15) Expressing SNR in decibels yields (1.16) This shows that the SNR is improved by 6 dB per bit. PCM voice telephony usually uses 8 bits, which implies a maximum SNR of 52.8 dB. The crest factor is defined as the peak amplitude of a waveform divided by its RMS value. Unfortunately for voice applications, the crest factor is usually very high, implying that the actual SNR is significantly less that the theoretical upper bound. Figure 1.10 shows another aspect of quantization noise, t