Digital Communication System Simulation

This project was developed for the Telecom Systems course at Harokopio University of Athens – Dept. of Informatics and Telematics.

This project, developed in Python, simulates a digital communication system using Pulse Amplitude Modulation (PAM). It is split into two parts: one for generating a PAM waveform and another for analyzing its spectral characteristics.

---

Project Structure

• PartA.py: Generates a random bit sequence, converts it into Gray-coded symbols, and creates the corresponding PAM waveform.
• PartB.py: Analyzes the spectral characteristics of the triangular pulse used in PartA.py, comparing analytical and numerical calculations for the power spectral density (PSD).
• README.md: This file.

---

Getting Started

Prerequisites

Make sure you have Python installed, along with the following libraries:

• numpy
• matplotlib

You can install them using pip:

pip install numpy matplotlib

How to Run

1. Generate a PAM Waveform: Run PartA.py and follow the on-screen prompts to input the number of samples per symbol (N) and the symbol duration (Ts). The script will generate a random bit sequence, convert it to symbols, and display the resulting PAM waveform.

python PartA.py

2. Analyze the Power Spectral Density: Run PartB.py to analyze the spectral properties of the triangular pulse. Similarly, you'll be prompted to enter N and Ts. The script will then plot the analytical and numerical power spectral density (PSD) for comparison.

python PartB.py

Key Features

PartA.py

• bits_to_gray_symbols(input_bits, p): Converts a bit sequence into a Gray-coded symbol sequence. Gray coding ensures that adjacent symbols differ by only a single bit, which minimizes bit errors during decoding.

• generate_pam_waveform(symbols, M, b, Ts, N): Creates the PAM waveform using a triangular pulse shape for each symbol.

• plot_waveform(waveform, Ts, N): Visualizes the generated PAM waveform over time.

PartB.py

• generate_pulse(Ts, N): Creates the triangular pulse shape p(t).

• power_spectral_density(p_t, Ts, N): Calculates the power spectral density (PSD) of the pulse both analytically (using the sinc function formula) and numerically (using the Fast Fourier Transform).

• Visualizations: Plots are generated to compare the analytical and numerical results for both the pulse spectrum ∣P(f)∣ and the PSD S_x(f).

Configuration

The main script in PartA.py is configured with the following parameters:

• p = 4: A parameter based on the author's student ID, influencing the number of bits per symbol.

• M = 2 ** (p + 3): The number of amplitude levels.

• b = 1: The scaling factor for the amplitude levels.

These parameters can be adjusted directly within the script to explore different system configurations.

Author

• Name: Exarchou Athos
• Student ID: it2022134
• Email: [email protected]

License

MIT License