PART -1
An analog signal is to be transmitted over a noisy channel and received at the receiver
Part1 (Q1). Analog to Digital converter.
- Choose the sampling rate, Quantization levels and encoding with suitable reasons .
Ans – The sampling rate used is - 4 , Quantization levels = 2^4 = 8 ;
* Code of Analog To Digital Converter -
Sr No. Code Comments
1. close all
2. clear all
3. clc
4. Fs = 200; Sampling frequency
5. T = 1/Fs; Sampling Period
6. t = 0:T:1; Time vector from 0 to 1
second
7. f = 10; Frequency of the analog
signal
8. x = sin(2*pi*f*t); Analog signal
9.
10. % Plotting the original analog signal
11. subplot(4,1,1);
12. plot(t, x);
13. xlabel('Time (s)');
14. ylabel('Amplitude');
15. title('Analog Signal');
16.
17. % Sampling
18. subplot(4,1,2);
19. stem(t, x, 'r', 'linewidth', 1.5);
20. xlabel('Time (s)');
21. ylabel('Amplitude');
22. title('Sampled Signal');
23.
24. % Quantization
25. bits = 4; Number of bits for
quantization
26. levels = 2^bits; Number of quantization
levels
27. quantized_signal = round((x + 1) * (levels - 1) / Quantize the analog signal
2);
28.
29. % Plotting the quantized signal
30. subplot(4,1,3);
31. stem(t, quantized_signal, 'b', 'linewidth', 1.5);
32. xlabel('Time (s)');
33. ylabel('Quantized Value');
34. title('Quantized Signal');
35.
36. % ADC Output
37. adc_output = zeros(size(quantized_signal));
38. for i = 1:length(quantized_signal)
39. adc_output(i) = quantized_signal(i) / (levels -
1);
40. end
41.
42. % Plotting the ADC output
43. subplot(4,1,4);
44. stairs(t, adc_output, 'g', 'linewidth', 1.5);
45. xlabel('Time (s)');
46. ylabel('ADC Output');
47. title('ADC Output');
48.
49. % Adjusting plot appearance
50. set(gcf, 'Position', [100, 100, 800, 600]);
51. subplot(4,1,1);
52. axis tight;
53.
54. % Displaying the figure
55. figure;
56.
57. % Plotting the original analog signal for
reference
58. plot(t, x, 'r', 'linewidth', 1.5);
59. xlabel('Time (s)');
60. ylabel('Amplitude');
61. title('Analog Signal (Reference)');
62. axis tight;
* Output Waveform of Analog To Digital Converter
Part1 (Q2). Code of Source Encoder –
The Encoding Scheme used is Pulse Code Modulation -
Sr. No. Code Comments
1. Close all
2. Clear all
3. clc
4. % Generate a continuous analog signal
5. Fs = 100; Sampling frequency
6. t = 0:1/Fs:1 ; Time vector
7. f = 5; Frequency of the signal
8. analog_signal = sin(2*pi*f*t); Signal
9.
10. % PCM Encoder
11. num_bits = 8; Number of bits for each
sample
12. quantized_signal = round(analog_signal *
(2^(num_bits-1)));
13.
14. % Display original and quantized signals
15. figure;
16. subplot(2,1,1);
15. plot(t, analog_signal);
16. title('Original Analog Signal');
17.
18. subplot(2,1,2);
19. stem(t, quantized_signal);
20. title('Quantized Signal');
21. xlabel('Time (s)');
22. ylabel('Quantized Value');
Output Waveform of Source Encoder –
Part1 (Q3). Code of Channel Encoder –
Sr. No. Code Comments
1. Close all
2. Clear all
3. clc Ans-
4. % Parameters Channel
5. n = 7; Total number of bits in a encoding is
codeword typically used to
6. k = 4; Number of information add redundancy
bits to the
7. message = randi([0, 1], 1, k); Generate random k-bit transmitted
message signal to aid in
8. error
9. % Channel encoding (Hamming code)
10. encoded_message = encode(message, n, k,
'hamming/binary'); detection and
11.
correction at the
12. % Display the original message and encoded
receiver . One
message
common
13. figure ;
14. subplot(2,2,2) approach is to
15. plot(message); Plotting original signal use error-
16. title('Original Message'); correcting
15. figure ; codes,
16. subplot(2,2,2) such
17. plot(encoded_message); Plotting encoded signal as Hamming
18. title('Encoded message'); codes . In this
19.
example ,demonstrating a simple (7,4) Hamming code for channel
encoding .
Output Waveform of Channel Encoder
Part1.(Q4) Code for Channel-
Sr. No. Code Comments
1. Close all
2. Clear all
3. clc
4. % Parameters
5. Fs = 1000; Sampling frequency
6. f = 10; Signal frequency
7. t = 0:1/Fs:1; Time vector
8.
9. % Generate analog signal (sine wave)
10. analog_signal = sin(2*pi*f*t);
11.
12. % Plot the analog signal
13. figure;
14. plot(t, analog_signal);
15. title('Analog Signal');
16. xlabel('Time');
15. ylabel('Amplitude');
16. % Parameters for noise
17. SNR_dB = 20; Signal-to-noise ratio
in dB
18. noise_power = var(analog_signal) / Noise Power
(10^(SNR_dB/10));
19.
20. % Generate Gaussian noise
21. noise = sqrt(noise_power) *
randn(size(analog_signal));
22.
23. % Add noise to the signal
24. noisy_signal = analog_signal + noise;
25.
26. % Plot the noisy signal
27. figure;
28. plot(t, noisy_signal);
29. title('Noisy Signal');
30. xlabel('Time');
31. ylabel('Amplitude');
32. % Design a simple low-pass filter
33. cutoff_frequency = 20 ; Adjust as needed
34. order = 4; Filter order
35.
36. % Design the filter
37. [b, a] = butter(order, cutoff_frequency / (Fs / 2));
38.
39. % Apply the filter to the received signal
40. filtered_signal = filter(b, a, noisy_signal);
41.
42. % Plot the filtered signal
43. figure;
44. plot(t, filtered_signal);
45. title('Filtered Signal');
46. xlabel('Time');
47. ylabel('Amplitude');
Output of Channel
Sr. Code Comments
No.
1. close all
2 clear all
3 clc
4 pkg load communications
5 M=8; No of levels
6 numsymbols=10000; No of symbols to be generated
7 bits=randi([0 M-1],1,numsymbols); random bit sequence
modulated_signal=pskmod(bits,M,pi/M); phase modulating the given bit
sequence
modulated_signal=awgn(modulated_signal,15,'measured'); adding white gaussian noise
demodulatedbits=pskdemod(modulated_signal,M,pi/M); demodulating the psk signal
incorrectsymbols=find(demodulatedbits~=bits) finding incorrect symbols in
demodulated data
scatterplot(modulated_signal) plotting constellation diagram
of modulated signal
scatterplot(modulated_signal);
hold on;
scatter(real(modulated_signal(incorrectsymbols)),
imag(modulated_signal(incorrectsymbols)),'r','filled');
%plotting constellation diagram of modulated signal and
incorrect data
ber=length(incorrectsymbols)/length(bits); Finding bit error rate
Part1 (Code 2 )
Part1 (Q5.) *Code for Channel Decoder
Sr. No. Code Comments
1. Close all
2. Clear all
3. clc
4. function decoded_data = * Output of
hamming_decoder(received_data) Channel
5. % Hamming Decoder (7,4) Decoder
6.
7. % Define the parity check matrix for (7,4) Hamming
code
8. H=[
9. 1 1 0 1 1 0 0;
10. 0 1 1 1 0 1 0;
11. 1 1 1 0 0 0 1;
12. ];
13.
14. % Split the received data into 7-bit blocks
15. received_blocks = reshape(received_data, 7,
length(received_data)/7)';
16.
15. % Initialize the decoded data matrix
16. decoded_data = [];
17.
18. % Decode each 7-bit block
19. for i = 1:size(received_blocks, 1)
20. received_block = received_blocks(i, :)';
21. syndrome = mod(received_block * H', 2);
22.
23. % Correct errors, if any
24. if sum(syndrome) > 0
25. error_position = bin2dec(num2str(syndrome'));
26. received_block(error_position) =
mod(received_block(error_position) + 1, 2);
27. end
28.
29. % Extract the original 4 bits
30. decoded_data = [decoded_data;
received_block(1:4)];
31. end
32.
33. % Convert the decoded data to a row vector
34. decoded_data = 'decoded_data';
35. end
36.
37. % Example Usage
38. received_data = [1 0 1 0 0 1 0 1 1 1 0 1 0 1 1 0 1 0 1 0 1 1 Received data
1 1 0 0 0 1 0 1 1 1 1 0 0 1 0];
39. decoded_output = hamming_decoder(received_data);
40.
41. % Display results
42. figure ;
43. subplot(2,1,1) ;
44. plot(received_data); Plotting
received data
45. title('Received Data');
Part1(Q6.) Code of SourceDecoder
Sr. No. Code Comments
1. Close all
2. Clear all
3. clc
4. % Generate a continuous analog signal
5. Fs = 100; Sampling Frequency
6. t = 0:1/Fs:1 ; Time Vector
7. f = 5; Siganl Frequency
8. analog_signal = sin(2*pi*f*t);
9.
10. % PCM Encoder
11. num_bits = 8;
12. quantized_signal = round(analog_signal * Defined Function
(2^(num_bits-1)));
13.
14. % Display original and quantized signals
15. figure;
16. subplot(2,1,1);
15. plot(t, analog_signal); Plotting analog signal
16. title('Original Analog Signal');
17.
18. subplot(2,1,2);
19. stem(t, quantized_signal);
20. title('Quantized Signal');
21. xlabel('Time (s)');
22. ylabel('Quantized Value');
23.
24. % Assume received PCM signal (after transmission over
a noisy channel)
25. received_pcm_signal =
quantized_signal(round(analog_signal * (2^(num_bits-
1))));
26. % Replace ... with your received PCM signal
27.
28. % Demodulate the PCM signal
29. demodulated_signal =
pcmdecode(received_pcm_signal);
30.
31. % Plot the demodulated signal
32. figure;
33. plot(demodulated_signal);
34. title('Demodulated Signal');
35. xlabel('Sample Number');
36. ylabel(‘Amplitude’)
Output waveform of Source Decoder
Sr. No. Code Comments
1. Close all
2. Clear all
3. clc
4. % Parameters
5. Fs = 200; Sampling
frequency
6. f = 10; Signal frequency
7. t = 0:1/Fs:1; Time vector
8.
9. % Generate an example analog signal (sine wave)
10. analog_signal = sin(2*pi*f*t);
11.
12. % Quantize the analog signal to PCM
13. num_bits = 8; % Number of bits for quantization
14. quantized_signal = round(analog_signal * (2^(num_bits-
1) - 1));
15.
16. % Digital-to-Analog Conversion using Interpolation
15. reconstructed_analog_signal =
interp1(1:length(quantized_signal), quantized_signal,
linspace(1, length(quantized_signal), length(t)),
'previous');
16.
17. % Plot the original analog signal, quantized PCM signal,
and reconstructed analog signal
18. figure;
19.
20. subplot(3, 1, 1);
21. plot(t, analog_signal);
22. title('Original Analog Signal');
23. xlabel('Time');
24. ylabel('Amplitude');
25.
26. subplot(3, 1, 2);
27. stem(quantized_signal);
28. title('Quantized PCM Signal');
29. xlabel('Sample Number');
30. ylabel('Amplitude');
31.
32. subplot(3, 1, 3);
33. plot(t, reconstructed_analog_signal);
34. title('Reconstructed Analog Signal from PCM');
35. xlabel('Time');
36. ylabel('Amplitude');
Part1(Q7.) Code of Digital to Analog Converter
Output Waveform for Digital To Analog Converter
