EXPERIMENT 4 PULSE CODE MODULATION

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1 EXPERIMENT 4 PULSE CODE MODULATION 1.0 OBJECTIVES 1.1 To generate sampled signal using SCILAB software. 1.2 To perform Pulse Code Modulation system using SCILAB. 2.0 EQUIPMENT/APPARATUS SCILAB Software 3.0 THEORY 3.1 Pulse Code Modulation Pulse Code Modulation (PCM) is the digitally encoded modulation technique that is commonly used for digital transmission. With PCM, the pulses are of fixed length and fixed amplitude. PCM is a binary system where a pulse or lack of pulse within a prescribed time slot represents either a logic 1 or a logic 0 condition. 3.2 PCM Block Diagram Figure 1 shows a simplified block diagram of a single-channel, simplex (one-way only) PCM system. The low-pass filter band-limited the frequency of the analog input signal to the maximum frequency in accordance with the sampling theorem. It is then sampled and converted those samples to a multilevel PAM signal. The sampled pulses (PAM samples) are rounded off to the nearest pre-determined level (quantized level) in the quantizer. Then the quantized samples are converted into groups according to the binary code in the encoder. These coded pulses are then modulated digitally in the modulator (modem) before being transmitted through the channel. 1

2 Digital Signal TRANSMITTER Analog Signal (i/p) Low Pass Filter (LPF) Sampler Quantizer Coder Digital Modulator Channel Analog Signal (i/p) Low Pass Filter (LPF) Expandor Decoder Demodulator Digital Signal RECEIVER Figure 1 : Simplified block diagram of a single-channel, simplex PCM transmission system Sampling Sampling is the process of taking samples of the analog input signal at a rate of Nyquist sampling frequency. The function of a sampling circuit in a PCM transmitter is to periodically sample the continually changing analog input voltage and convert those samples to a series of constant-amplitude pulses that can more easily be converted to binary PCM code Quantization Quantization is the process of converting an infinite number of amplitude possibilities (analog signal samples) to a finite number of conditions (predetermined discrete levels). The number of quantization levels, L, deps on the number of bits per sample, n, used to code the analog signal where L = 2 n (1) The magnitude of the stepsize of the quantization levels is called resolution, ΔV. The resolution deps on the maximum voltage, V max, and the minimum voltage, V min, of the information signal, where V V max V min L 1 (2) 2

3 3.2.3 Encoding Encoding is a process where each quantized sample is digitally encoded into n-bits codeword, where n log 2 L (4.5) where n = number of bits/sample L = number of quantization levels 3

4 EXAMPLE : Consider a signal x(t) = sin 2π5t is to be quantized into 8 levels. The number of samples is Write a command using Scilab to plot the following signal : (i) Original signal (ii) Quantized signal Determine the encoding bit for each sample. SOLUTION : clc; close; t = 0:0.001:1; x = sin(2*%pi*5*t); L = 8; //quantization xmax = max(abs(x)); xq = x/xmax; en_code = xq; d = 2/L; q = d*[0:l-1]; q = q-((l-1)/2)*d; for i = 1:L xq(find(((q(i)-d/2)<= xq)&(xq<=(q(i)+d/2))))=q(i).*ones(1,length(find(((q(i)- d/2)<=xq)&(xq<=(q(i)+d/2))))); en_code(find(xq == q(i)))= (i-1).*ones(1,length(find(xq == q(i)))); xq = xq*xmax; plot2d2(t*2*%pi,x); plot2d2(t*2*%pi,xq,5); (iii) Encoding n = log2(l); c = zeros(length(x),n); for i = 1:length(x) for j = n:-1:0 if(fix(en_code(i)/(2^j))==1) c(i,(n-j)) =1; en_code(i) = en_code(i)-2^j; disp(c) 4

5 EXERCISE 1) A sinusoidal input signal, m(t) having an amplitude of 1V is sampled at 1000 samples and the samples are quantized to 16 evenly spaced levels. (a) Use Scilab to plot the following signal : (i) (ii) Original signal Quantizing signal. (b) Determine the PCM code using SCILAB. 2) A sinusoidal input signal, m(t) having an amplitude of 1V is sampled at 100 samples and the samples are quantized to 8 evenly spaced levels. Use Scilab to plot the following signal : (a) Use Scilab to plot the following signal : (iii) Original signal (iv) Quantizing signal. (b) Determine the PCM code using SCILAB. (c) Determine the voltage of input signal that represented by 010, 011, and Report *Your report should include: Result, Discussion, Conclusion, Appix. 5

CHAPTER 4. PULSE MODULATION Part 2

CHAPTER 4. PULSE MODULATION Part 2 CHAPTER 4 PULSE MODULATION Part 2 Pulse Modulation Analog pulse modulation: Sampling, i.e., information is transmitted only at discrete time instants. e.g. PAM, PPM and PDM Digital pulse modulation: Sampling