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    DC Lab 07

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    photoid user1
    The document demonstrates pulse code modulation (PCM) using MATLAB. It shows the encoding and decoding of an analog signal using an 8-bit PCM system with 8 samples per period. In the encoding, the analog signal is sampled, quantized to 8-bit levels, and converted to a binary code. The maximum quantization error between the original and quantized signals is determined. In the decoding, the binary code is converted back to decimal indices, used to recover the quantized values, and thus reconstruct the original analog signal. The original and recovered signals are plotted for comparison.

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    DC Lab 07

    Uploaded by

    photoid user1
    20 views10 pages
    The document demonstrates pulse code modulation (PCM) using MATLAB. It shows the encoding and decoding of an analog signal using an 8-bit PCM system with 8 samples per period. In the encoding, the analog signal is sampled, quantized to 8-bit levels, and converted to a binary code. The maximum quantization error between the original and quantized signals is determined. In the decoding, the binary code is converted back to decimal indices, used to recover the quantized values, and thus reconstruct the original analog signal. The original and recovered signals are plotted for comparison.

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    The document demonstrates pulse code modulation (PCM) using MATLAB. It shows the encoding and decoding of an analog signal using an 8-bit PCM system with 8 samples per period. In the encoding, the analog signal is sampled, quantized to 8-bit levels, and converted to a binary code. The maximum quantization error between the original and quantized signals is determined. In the decoding, the binary code is converted back to decimal indices, used to recover the quantized values, and thus reconstruct the original analog signal. The original and recovered signals are plotted for comparison.

    Copyright:

    © All Rights Reserved
    Download as DOCX, PDF, TXT or read online from Scribd
    Download as docx, pdf, or txt
    20 views10 pages

    DC Lab 07

    Uploaded by

    photoid user1
    The document demonstrates pulse code modulation (PCM) using MATLAB. It shows the encoding and decoding of an analog signal using an 8-bit PCM system with 8 samples per period. In the encoding, the analog signal is sampled, quantized to 8-bit levels, and converted to a binary code. The maximum quantization error between the original and quantized signals is determined. In the decoding, the binary code is converted back to decimal indices, used to recover the quantized values, and thus reconstruct the original analog signal. The original and recovered signals are plotted for comparison.

    Copyright:

    © All Rights Reserved
    Download as DOCX, PDF, TXT or read online from Scribd
    Download as docx, pdf, or txt
    of 10

    DEPARTMENT OF COMPUTER &

    SOFTWARE ENGINEERING
    COLLEGE OF E&ME, NUST,
    RAWALPINDI

    EC-431 Digital Communication

    LabNumber 07

    NIMRA AKMAL
    CE 41 B
    288608
    Lab # 07: Demonstration of Pulse Code Modulation

    Objective:
    To demonstrate the principle of PCM (pulse code modulation) and implementation of a PCM
    based digital communication system.

    Tasks:

    1. Plot a difference delta of the sampled signal and quantized signal in Fig. 3. Compare
    them using different line specs on same graph. How much is the maximum quantization
    error?
    clc;
    close all;
    clear all;
    n=input('Enter n value for n-bit PCM system : ');
    n1=input('Enter number of samples in a period : ');
    L=2^n;

    % % Signal Generation + Sampling Operation


    x=0:2*pi/n1:4*pi; %4pi to plot two cycles for visibility and n1 number
    of samples per period have to be selected

    Vmax=8;
    s=Vmax.*sin(x);%Vmax.*sin(x)
    subplot(4,1,1);
    plot(s);
    title('Source Analogue Signal');
    ylabel('Amplitude');
    xlabel('Time');
    subplot(4,1,2);
    stem(s);grid on; title('Sampled Signal'); ylabel('Amplitude');
    xlabel('Time');

    %Quantizer for our PCM encoder case


    Vmin=-Vmax;
    delta=(Vmax-Vmin)/L; %step size delta
    part=Vmin:delta:Vmax; % Levels are
    between Vmin and Vmax with difference of delta- Without quantization
    code=Vmin-(delta/2):delta:Vmax+(delta/2); % Contains
    Quantized values
    [ind,q]=quantiz(s,part,code);
    % Now, ind will contain index number and q contain quantized values
    l1=length(ind);
    l2=length(q);

    for i=1:l1
    if(ind(i)~=0) % To make index as binary decimal so started
    from 0 to N
    ind(i)=ind(i)-1;
    end
    i=i+1;
    end
    for i=1:l2
    if(q(i)==Vmin-(delta/2)) % To make quantized value in between the
    levels
    q(i)=Vmin+(delta/2);
    end
    end
    subplot(4,1,3);
    stem(q,'r*');grid on; % Display the Quantized values
    title('Quantized Signal');
    ylabel('Amplitude');
    xlabel('Time');

    % subplot(4,1,4);
    % stem(s);
    % hold on
    % stem(q,'r*');

    subplot(4,1,4);
    diff= s-q;
    stem(diff);
    title('Difference of s and q');
    mx=max(diff);
    2. Run your whole PCM encoder code (whose output in Fig; 3 and 4) for a 8-bit PCM i.e.,
    n=8. Use a sampling period of 8 also i.e., n1 =8. Plot Fig. 3 and 4 again as above. Also
    give the values of ind and code matrices as mentioned in the PCM encoding section
    above.
    clc;
    close all;
    clear all;
    n=input('Enter n value for n-bit PCM system : ');
    n1=input('Enter number of samples in a period : ');
    L=2^n;

    % % Signal Generation + Sampling Operation


    x=0:2*pi/n1:4*pi; %4pi to plot two cycles for visibility and n1 number of
    samples per period have to be selected

    Vmax=8;
    s=Vmax.*sin(x);%Vmax.*sin(x)
    subplot(4,1,1);
    plot(s);
    title('Source Analogue Signal');
    ylabel('Amplitude');
    xlabel('Time');
    subplot(4,1,2);
    stem(s);grid on; title('Sampled Signal'); ylabel('Amplitude');
    xlabel('Time');

    %Quantizer for our PCM encoder case


    Vmin=-Vmax;
    delta=(Vmax-Vmin)/L; %step size delta
    part=Vmin:delta:Vmax; % Levels are
    between Vmin and Vmax with difference of delta- Without quantization
    code=Vmin-(delta/2):delta:Vmax+(delta/2); % Contains
    Quantized values
    [ind,q]=quantiz(s,part,code);
    % Now, ind will contain index number and q contain quantized values
    l1=length(ind);
    l2=length(q);

    for i=1:l1
    if(ind(i)~=0) % To make index as binary decimal so started
    from 0 to N
    ind(i)=ind(i)-1;
    end
    i=i+1;
    end
    for i=1:l2
    if(q(i)==Vmin-(delta/2)) % To make quantized value in between the levels
    q(i)=Vmin+(delta/2);
    end
    end
    subplot(4,1,3);
    stem(q,'r*');grid on; % Display the Quantized values
    title('Quantized Signal');
    ylabel('Amplitude');
    xlabel('Time');
    % subplot(4,1,4);
    % stem(s);
    % hold on
    % stem(q,'r*');

    subplot(4,1,4);
    diff= s-q;
    stem(diff);
    title('Difference of s and q');

    figure
    code=de2bi(ind,'left-msb');
    k=1;
    for i=1:l1
    for j=1:n
    coded(k)=code(i,j);
    % convert code matrix to a coded row vector
    j=j+1;
    k=k+1;
    end
    i=i+1;
    end
    subplot(2,1,1); grid on;
    stem(coded);
    % Display the encoded signal
    [a b]= size(code);
    axis([0 a*b -1 2]); title('Encoded Signal');
    ylabel('Amplitude');
    xlabel('Time Index');

    subplot(2,1,2); grid on;


    stairs(coded);
    % Display the encoded signal
    [a b]= size(code);
    axis([0 a*b -1 2]);
    %title('Encoded Signal');
    ylabel('Amplitude');
    xlabel('Time Index');
    3. Demodulation of PCM signal
    Demodulate the PCM encoded signal above to recover the original analogue signal. Plot
    the two on same graph with different color and line specs to compare results.

    Hint: Use reshape to convert the coded vector above and use bi2dec to convert the binary
    indices back to decimal. Then get back the quantized value using,
    q =delta*index + Vmin + (delta/2);
    clc;
    close all;
    clear all;
    n=input('Enter n value for n-bit PCM system : ');
    n1=input('Enter number of samples in a period : ');
    L=2^n;

    % % Signal Generation + Sampling Operation


    x=0:2*pi/n1:4*pi; %4pi to plot two cycles for visibility and n1 number
    of samples per period have to be selected

    Vmax=8;
    s=Vmax.*sin(x);%Vmax.*sin(x)
    subplot(4,1,1);
    plot(s);
    title('Source Analogue Signal');
    ylabel('Amplitude');
    xlabel('Time');
    subplot(4,1,2);
    stem(s);grid on; title('Sampled Signal'); ylabel('Amplitude');
    xlabel('Time');

    %Quantizer for our PCM encoder case


    Vmin=-Vmax;
    delta=(Vmax-Vmin)/L; %step size delta
    part=Vmin:delta:Vmax; % Levels are
    between Vmin and Vmax with difference of delta- Without quantization
    code=Vmin-(delta/2):delta:Vmax+(delta/2); % Contains
    Quantized values
    [ind,q]=quantiz(s,part,code);
    % Now, ind will contain index number and q contain quantized values
    l1=length(ind);
    l2=length(q);

    for i=1:l1
    if(ind(i)~=0) % To make index as binary decimal so started
    from 0 to N
    ind(i)=ind(i)-1;
    end
    i=i+1;
    end
    for i=1:l2
    if(q(i)==Vmin-(delta/2)) % To make quantized value in between the
    levels
    q(i)=Vmin+(delta/2);
    end
    end
    subplot(4,1,3);
    stem(q,'r*');grid on; % Display the Quantized values
    title('Quantized Signal');
    ylabel('Amplitude');
    xlabel('Time');

    % subplot(4,1,4);
    % stem(s);
    % hold on
    % stem(q,'r*');

    subplot(4,1,4);
    diff= s-q;
    stem(diff);
    title('Difference of s and q');

    figure
    code=de2bi(ind,'left-msb');
    k=1;
    for i=1:l1
    for j=1:n
    coded(k)=code(i,j);
    % convert code matrix to a coded row vector
    j=j+1;
    k=k+1;
    end
    i=i+1;
    end
    subplot(2,1,1); grid on;
    stem(coded);
    % Display the encoded signal
    [a b]= size(code);
    axis([0 a*b -1 2]); title('Encoded Signal');
    ylabel('Amplitude');
    xlabel('Time Index');

    subplot(2,1,2); grid on;


    stairs(coded);
    % Display the encoded signal
    [a b]= size(code);
    axis([0 a*b -1 2]);
    %title('Encoded Signal');
    ylabel('Amplitude');
    xlabel('Time Index');

    % Demodulation of PCM encoded signal


    decode = reshape(coded, n, length(coded)/n)';
    index = bi2de(decode, 'left-msb')';
    q = delta*index + Vmin + (delta/2);

    % Plot the quantized values and recovered analog signal


    figure
    subplot(3,1,1)
    stem(q, 'r*');
    title('Recovered Signal')
    ylabel('Amplitude')
    xlabel('Time Index')

    subplot(3,1,2)
    plot(q, 'r*'); hold on
    plot(s, 'b--')
    title('Quantized Signal and Recovered Analog Signal')
    ylabel('Amplitude')
    xlabel('Time')
    Ind:

    Index

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