ELEMENTS IF PULSE CODE MODULATION – PCM

1.  Objective
        Introduction to PCM and Analog-to-Digital & Digital-to-Analog Conversion.
2.  General Information
        In Pulse Modulation, analog message is transmitted in discrete time. First of all, sampling
of the message signal should be performed.Considering the sampling process, the sampled signal appears as a train of samples which is a form of PAM (Pulse Amplitude Modulation) signal. When M levels are used to quantize this signal,this modulation is called M-PAM. If those pulses were converted to digital numbers, then the train of numbers so generated would be called as Pulse Code Modulated – PCMsignal. In PCM,
modulation process is executed in three steps:
1.  Sampling
2.  Quantizing
3.  Coding
These steps are shown in Figure  with a block diagram: 

As stated before, in PCM, the information signal x(t) is first sampled with the appropriate
sampling frequency (sampling frequency fs ≥2×highest frequency of the information signal (fx) ), then the sampled levels are quantized to appropriate quantization levels. In the last step, each quanta level is demonstrated by a two-code word, that is by a finite number of {0,1} sequence. After this step, the signal is called as PCM wave. If the max and min amplitude values of information signal x(t) are Amaxand Amin, respectively, and if n-digit code words will be used, then the quantizing interval/pace “a” becomes:

 

In quantizing process, “which quanta region does the sample belong to” is an important question. The sample value isrounded to the closest quanta level. Later the quantized signal is encoded and the signal is matched with code words. In two-word number system, +V volt pulse can be sent for ‘1’s, and space/no volt is sent for ‘0’s to transmit the code.
As another method, +V volt pulse is sent for ‘1’s, and –V volt pulse is sent for ‘0’s. A
guide gap (tg) is kept between two pulses. An example to the PCM steps explained up to
here is given in Figure 2.

In Figure – 2, the signal is divided into 16 amplitude levels (0-1.5) between its max and
min values. Therefore, n=4 and the quantizing pace a =0.1. If the quantizing levels are selected equally, then this is called as “linear quantizing”. 

Figure 3 shows an example to the linear quantizing.

In the converter shown in Figure- 4, VAis compared to VBvoltage during the sampling period Tsas the output of the D/A converter. If VA > VB, then the comparator output is logic 1 and the gate is open. In this case, the coming clock pulse reaches the counter and the counting continues. Output of D/A increases by 1 step, as each step comes. Sometime later VB voltage catches the VAand starts to become larger. At that time, output of the comparator reduces to ‘0’ and the gate is closed. Counting process has stopped. At that time, Q outputs give the code corresponding to the input voltage. When the sampling period ends, the counter resets and the sameprocess starts for the second sample. The converter given in Figure 4 is only used for positive voltages. If both negative and positive voltages are required to be converted, then the circuitry given in Figure 5 is used. 

3. Experiment Set
•  PC & LabView Software
4. Experimental Procedure
•  In this experiment an analog signal will be sampled and according to the specified
word length it will be digitized.
•  Generate a sinusoidal analog signal so that the display duration Tand the duration
between each sample dTcan be changed externally by the user.
•  Sample this analog signal with a sample frequency that can be changed by the user
while the program is running.
•  Display both the analog signal and the samples in a single waveform graph screen.
•  Define a “word-length” control in the front panel of the “*.vi” program you
design, to specify the quantizing levels. The word length should be selectable
externally by the user.
•  Try to recover the analog signal from the quantized digital signal and display it in
a waveform graph screen.