Telecommunication I Course Project

Course: Telecommunication I (IUST)
Semester: 402-2
Student: Seyed Alireza Mirabedini

📋 Table of Contents

• Overview
• Project Structure
• Part 1: Audio Signal Analysis
  • Audio Signal Spectrum
  • White Noise Analysis
  • Quadrature Noise Component
  • Noise and Phase Shift Combination
  • Phase Compensation
  • Filtering Analysis
• Part 2: Simulink AM Modulation
  • AM Modulator
  • AM Detector
• Files Description
• Requirements
• Usage
• Results

🎯 Overview

This project investigates the effects of noise, phase shift, and filtering on audio signals, and implements AM (Amplitude Modulation) modulator and detector systems using MATLAB/Simulink. The project consists of two main parts:

1. Audio Signal Processing: Analysis of audio signals with noise, phase shifts, and various filtering techniques
2. AM Modulation System: Design and simulation of AM modulator and detector circuits

📁 Project Structure

.
├── Main.m                              # Main MATLAB script for Part 1
├── A.m                                 # Script to create structure A for AM modulator
├── B.m                                 # Script to create structure B for AM detector
├── Am.slx                              # Simulink model: AM Modulator
├── AmDet.slx                           # Simulink model: AM Detector
├── Avaz on Rumi Sonnet.mp3            # Input audio file (Rumi sonnet)
├── Am_032.wav, Am_100.wav, Am_150.wav # AM modulated outputs (m=0.32, 1.0, 1.5)
├── Det_032.wav, Det_100.wav, Det_150.wav # AM detector outputs (before filter)
├── Det_F_032.wav, Det_F_100.wav, Det_F_150.wav # AM detector outputs (after filter)
├── Channel.wav                         # Phase compensated signal
├── Channel_Filtered.wav               # Filtered before phase compensation
├── Channel_After_Filtered.wav         # Filtered after phase compensation
├── shifted_audio.wav                  # Phase-shifted audio
├── shifted_audio_with_noise.wav       # Phase-shifted audio with noise
├── Compare_1.png, Compare_2.png       # Comparison plots
├── doc.pdf                            # Project documentation (PDF)
└── doc.docx                           # Project documentation (DOCX)

🔊 Part 1: Audio Signal Analysis

Audio Signal Spectrum

The project begins by analyzing an audio file containing a segment of Rumi's poetry recitation. The audio signal is loaded and its Fourier transform is computed to visualize the frequency spectrum.

message = importdata("Avaz on Rumi Sonnet.mp3");
F = linspace(0, message.fs, nfft);
msg_ft_data = fft(message.data, nfft);
msg_absft_data = abs(msg_ft_data);

plot(F(1:nfft/2), msg_absft_data(1:nfft/2));
xlabel("Frequency");
ylabel("Domain");
title("Frequency - Domain Plot")

Observation: The spectrum analysis shows that the audio signal is a baseband signal.

White Noise Analysis

White Gaussian noise is generated and added to the signal to study its effects:

white_noise = wgn(length(message.data), 2, -20);
white_noise_ft = fft(white_noise, nfft);
white_noise_ftabs = abs(white_noise_ft);

Observation: The spectrum shows that white noise contains all frequency components uniformly distributed.

Quadrature Noise Component

The quadrature component of noise is extracted using the Hilbert transform:

white_noise_Qd = imag(hilbert(white_noise, nfft));

Observation: The imaginary part of the Hilbert transform represents the quadrature component of the noise.

Noise and Phase Shift Combination

Phase shift is applied to the signal along with noise addition:

signal_ft_shifted = msg_ft_data .* exp(4i*pi/9);
signal_ft_shifted_WithNoise = signal_ft_shifted + white_noise_ft;
signal_ft_WithNoise = msg_ft_data + white_noise_ft;
signal_shifted = real(ifft(signal_ft_WithNoise));
audiowrite('shifted_audio_with_noise.wav', signal_shifted, message.fs);

Observation: While white noise is audible, phase shift alone is not perceptible. However, when combined, the changes become noticeable.

Phase Compensation

Phase compensation is performed to restore the original signal:

channel_ft = signal_ft_WithNoise .* exp(-4i*pi/9);
channel_phase = angle(channel_ft);
channel_abs = abs(channel_ft);
audiowrite('Channel.wav', real(ifft(channel_ft)), message.fs);

Filtering Analysis

Two filtering approaches are compared:

1. Filtering Before Phase Compensation

Filtered = lowpass(ifft(signal_ft_WithNoise), 16000, 44100);
Filtered_ft = fft(Filtered, nfft);
Filtered_channel = Filtered_ft .* exp(-4i*pi/9);
audiowrite('Channel_Filtered.wav', real(ifft(Filtered_channel)), message.fs);

2. Filtering After Phase Compensation

Filtered_After = lowpass(real(ifft(channel_ft)), 16000, 44100);
Filtered_After_ft = fft(Filtered_After, nfft);
audiowrite('Channel_After_Filtered.wav', real(ifft(Filtered_After_ft)), message.fs);

Observation: Analysis shows that the first 16 kHz is the most important frequency range. Filtering before phase compensation produces better results with reduced noise.

📡 Part 2: Simulink AM Modulation

AM Modulator

The AM modulator is implemented in Simulink (Am.slx) with modulation index calculated as:

μ = 0.2 + (24/200) = 0.32

The modulator is tested with three different modulation indices:

• m = 0.32
• m = 1.0
• m = 1.5

Observation: The modulated output is an unintelligible sound where only the beat patterns are distinguishable.

Output Files: Am_032.wav, Am_100.wav, Am_150.wav

AM Detector

The AM detector circuit is implemented using SimScape in Simulink (AmDet.slx). It demodulates the AM signal and includes filtering for noise reduction.

Key Findings:

• The output signal is successfully converted back to baseband
• Some noise is present in the output
• A low-pass filter significantly improves output quality
• Higher modulation index (m) results in better signal-to-noise ratio

Output Files:

• Before filtering: Det_032.wav, Det_100.wav, Det_150.wav
• After filtering: Det_F_032.wav, Det_F_100.wav, Det_F_150.wav

📋 Files Description

File	Description
Main.m	Main MATLAB script implementing audio signal processing
A.m	Creates structure A for AM modulator input
B.m	Creates structure B for AM detector analysis
Am.slx	Simulink model for AM modulator
AmDet.slx	Simulink model for AM detector
Avaz on Rumi Sonnet.mp3	Input audio file
Am_*.wav	AM modulated signals at different modulation indices
Det_*.wav	Demodulated signals (before filter)
Det_F_*.wav	Demodulated signals (after filter)
Channel*.wav	Various filtered and phase-compensated signals
shifted_audio*.wav	Phase-shifted audio signals
Compare_*.png	Comparison plots

🔧 Requirements

• MATLAB (R2019b or later recommended)
• Simulink
• Signal Processing Toolbox
• SimScape (for AM detector circuit simulation)
• Audio System Toolbox

🚀 Usage

Running Part 1 (Audio Signal Processing)

% Run the main script
run('Main.m')

This will generate various plots and audio files showing the effects of noise, phase shift, and filtering.

Running Part 2 (Simulink AM Modulation)

1. Open MATLAB and navigate to the project directory
2. Run A.m to create input structure for the modulator:

   run('A.m')

3. Open and run the AM modulator model:

   open('Am.slx')

4. Run B.m to create structure for detector analysis:

   run('B.m')

5. Open and run the AM detector model:

   open('AmDet.slx')

📊 Results

Part 1 Conclusions

• The input audio signal is confirmed to be a baseband signal
• White noise uniformly affects all frequency components
• Phase shift alone is not audible but becomes noticeable when combined with noise
• Lowpass filtering at 16 kHz cutoff effectively reduces noise
• Filtering before phase compensation produces superior results compared to filtering after

Part 2 Conclusions

• AM modulation successfully implemented for three different modulation indices
• Higher modulation index (m) results in better signal quality and SNR
• The detector circuit successfully demodulates the AM signal
• Post-detection lowpass filtering significantly improves audio quality
• The modulation index of 1.5 provides the best output signal relative to noise

👨‍🎓 Author

Seyed Alireza Mirabedini
Student ID: 401414024
Iran University of Science and Technology (IUST)

📄 License

This project is part of academic coursework. See LICENSE for details.