A PCM GENERATOR OR TRANSMITTER
In the last article, we had an overview of the elements of a PCM system (i.e., transmitter, transmission-path and receiver). In this section, we shall discuss the PCM generator (i.e., transmitter) from a practical point of view. Figure 4.3 shows a practical block diagram of a PCM generator.
DIAGRAM
FIGURE 4.3 A practical PCM generator
In PCM generator of figure 4.3, the signal x(t) is first passed through the low-pass filter of cutoff frequency fm Hz. This low-pass filter blocks all the frequency components which are lying above fm Hz.*
This means that now the signal x(t) is bandlimited to fm Hz. The sample and hold circuit then samples this signal at the rate of fs. Sampling frequency fs is selected sufficiently above nyquist rate to aviod aliasing i.e.,
fs 2fm
In figure 4.3, the output of sample and hold circuit is denoted by x(nTs). This signal x(nTs) is discrete in time and continuous in amplitude. A q-level quantizer compares input x(nTs) with its fixed digital levels. It assigns any one of the digital level to x(nTs) with its fixed digital levels. It then assigns any one of the digital level to x(nTs) which results in minimum distortion or error. This error is called quantization error. Thus, output of quantizer is a digital level called xq(nTs).
Now, the quantized signal level xq(nTs) is given to binary encoder. This encoder converts Input signal to ‘v’ digits binary word. Thus xq(nTs) is converted to ‘v binary hits. This encoder is also known as digitizer.
* Recall that this filter is used to avoid aliasing.
NOTE: It may be noted that it is not possible to transmit each bit of the binary word separately on transmission line. Therefore `v’ binary digits are converted to serial bit stream to generate single baseband signal. In a parallel to serial converter, usually a shift register does this job. The output of PCM generator is thus a single baseband signal of binary bits.
Also, an oxcillator generates the clocks for sample and hold circuit and parallel to serial converter. In the pulse code modulation generator discussed above, sample and hold, quantizer and encoder combinely form an analog to digital converter (ADC).
4.6 PCM TRANSMISSION PATH
| DO YOU KNOW? |
| PCM requires that the amplitude of each sample of a signal be converted to a binary number. The more bits used for the number, the greater the accuracy, but the greater the bit rate required. |
The path between the PCM transmitter and PCM receiver over which the PCM signal travel, is called as PCM transmission path and it is as shown in figure 4.4. The most important feature of PCM system lies in its ability to control the effects of distortion and noise when the PCM wave travels on the channel. PMC accomplishes this capacity by means of using a chain of regenerative repeaters as shown in figure 4.4. Such repeaters are spaced close enough to each other on the transmission path. The regenerative performs three basic operations namely equalization, timing and decision making. Hence, each repeater actually reproduces the clean noise free PCM signal from the PCM signal distorted by the channel noise. This improves the performance of PCM in presence of noise.
DIAGRAM
FIGURE 4.4 PCM transmission path.
4.6.1. Block Diagram of a Repeater
Figure 4.5 shows the block diagram of a regenerative repeater.
The amplitude equalizer shapes the distorted PCM wave so as to compensate for the effects of amplitude and phase distortions. The timing circuit produces a periodic pulse train which Is derived from the input PCM pulses. This pulse train is then applied to the decision making device. The decision making device uses this pulse train for sampling the equalized PCM pulses. The, sampling is carried out at the instants where the signal to noise ratio is maximum.
DIAGRAM
FIGURE 4.5 Block diagram of a regenerative repeater.
The decision device makes a decision about whether the equalized PCM wave at its input has a 0 value or 1 value at the instant of sampling. Such a decision is made by comparing equalized PCM with a reference level called decision threshold as illustrated in figure 4.6. At the output of the decision device, we get a clean PCM signal without any trace of noise.
DIAGRAM
FIGURE 4.6 Waveforms of a regenerative repeater.
4.7 PCM RECEIVER
In this section, we shall discuss a PCM receiver from practical point of view. Figure 4.7(a) shows the block diagram of PCM receiver and figure 4.7(b) shows the reconstructd signal. The regenerator at the start of PCM receiver reshapes the pulse and removes the noise. This signal is then coverted to parallel digital words for each sample.
DIAGRAM
FIGURE 4.7 (a) PCM receiver (b) Reconstructed waveform.
Now, the digital word is converted to its analog value denoted as xq(t) with the help of a sample and hold circuit. This signal, at the output of sample and hold circuit, is allowed to pass through a lowpass reconstruction filter to get the appropriate origianl message signal denoted as y(t).
NOTE: As shown in reconstructed signal of figure 4.7 (b), it is impossible to reconstruct exact original signal x(t) because of permanent quantization error introduced during quantization at the transmitter. In fact, this quantization error can be reduced by increasing the binary levels. This is equivalent to increasing binary digits (bits) per sample. But increasing bits ‘v’ increases the singnaling rate as well as transmission bandwidth as we have observed in last article. Therefore the choice of these parameters is made, in such. a manner that noise due to quantization error (i.e., also called as quantization noise) is in tolerable limits.
4.8 QUANTIZER
As discussed earlier, a q-level quantizer compares the discrete-time input x(nTs) with its fixed digital levels. It assigns any one of the digital level to x(nTs) with its fixed digital levels. It then assigns any one of the digital level to x(nTs) which results in minimum distortion or error. This error is called quantization error. Thus, the output of a quantizer is a digital level called xq(nTs).
4.8.1. Classification of Quantization Process
Basically, quantization process may be classified as follows :
DIAGRAM
The quantization process can be classified into two types as under:
(i) Uniform quantization
(ii) Non-uniform quantization.
This classification is based on the step size as defined earlier.
(i) Uniform Quantizer
A uniform quantizer is that type of quantizer in which the ‘step size’ remains same throughout the input range.
(ii) Nonuniform Quantizer
A non-uniform quantizer is that type of quantizer in which the ‘step-size’ varies according to the input signal values.
4.8.2. A Uniform Quantizer
As discussed earlier, a quantizer is called as an uniform quantizer if the step size remains constant throughout the input range.
4.8.2.1. Types of Uniform Quantizer (U.P. Tech, Sem. Exam., 2004-2005) (05 marks)
There are two types of uniform quantizer as under:
(i) Symmetric quantizer of the midtread type
(ii) Symmetric quantizer of the midrise type
Basically, quantizers can be of a uniform or nonuniform type. In a uniform quanitizer, the representation levels are uniformly spaced; otherwise, the quantizer is
nonuniform. Now, let Us consider only uniform quantizers, nonuniform quantizer shall be considered later on.
The quantizer characteristic can also be midtread or midrise type. Figure 4.8(b) shows the input-output characteristic of a uniform quanitizer of the midtread type, which is so called because the origin lies in the middle of a tread of the staircaselike graph. Figure 4.8(b) shows the corresponding input-output characteristic of a uniform quantizer of the midreise type, in which the origin lies in the midlle of a arising part of the stairceaselike graph. It may be noted that both the midtreat and midrise types of uniform quantizer illustrated in figure 4.8 are symmetric about the origin.
DIAGRAM
FIGURE 4.8 Two type of Uniform quantization : (a) Midtread, and (b) Midrise.
4.9 WORKING PRINCIPLE OF QUANTIZER
In this section, let us see how uniform quantization takes place. For this purpose, we shall consider uniform quantizer of midrise type. Figure 4.9(a) shows the transfer characteristics of a uniform quantizer of midrise type. In figure 4.9(a), let us assume that the input to the quantizer x(nTs) varies from – 4 D. Here ‘D’ is the step size.
Thus, input x(nTs) can take any value between – 4 D to + 4 D. Now, the fixed digital levels are avilable at ±. These levels arre avialable at quantizer because of its characteristics.
Hence, according to figure 4.9(a), we have
If x(nTs) = 4 D, then xq (nTs) =
and if x(nTs) = -4D, then xq (nTs) =
Thus, it may be observed from figure 4.9(b) that maximum quantization error would be .
Form above, we conculde that quantization error may be expressed as
here ‘ represents the quantization error
Now, when x(nTs) = 0, quantizer will assign any one of the nearest binary levels i.e., either D/2 or -D/2. If D/2 is assigned, then quantization error will be,
DIAGRAM
| DO YOU KNOW? |
| With a uniform quantizer, weak signals would experience a 40-dB poorer SNR than that of strong signals. The standard telephone technique of handling the large range of possible input signal levels is to use a logarithmic-compressed quantizer instead of a uniform one. |
FIGURE 4.9 (a) Transfer characteristic of a quantizer (b) Variation of quantization error with input -0 = D/2
From figure 4.9(a), it may also be observed that
for EQUATION
or EQUATION
This means that the maximum quantization error will be ±D/2.
In other words, maximum quantization error is given by
A UNIFORM QUANTIZER WITH INCORRECT QUANTIZATION Characteristics
The quantizer discussed in last section is known as uniform quantizer since the step size remains same throughout the input range. Also, if step size varies according to the input, then quantizer is known as non uniform quantizer. The reason for taking the digital levels at D/2, ±…. etc. is to reduce the quantization error. This has been illustrated in figure 4.10. Hence, there are two possible characteristics as shwon in figure 4.10(a). That is one characteristic ‘sA’ with thick line and second characteristic ‘B’ with thin line. It may be observed that for characteristic ‘A’, we have
DIAGRAM
FIGURE 4.10. (a) Incorrect quantization characteristic (b) Increased quantization error.
If 0 <x(nTs) <D; then output xq (nTs) = D
or 2D < x (nTs) < 3 D; then output xq (nTs) = 3D
Therefore, the maximum quantization error will be euqal to D as shown in figure 4.10(b). Similarly for characteristic ‘B’ maximum quantization error is equal to -D. The doted line shows actual transfer characteristic which passes through origin for characteristic show in figure 4.10(a). On the other hand, it does not pass through characteristic of figure 4.10(a). Hence, the digital levels are taken at ± D/2, ± etc. It provides correct quantization characteristic sand reduces quantization error.