Communication Systems Simulations

This repository contains solutions for four sets of communication systems homework problems. Each homework set focuses on different aspects of signal processing and modulation techniques. Below is an overview of each homework set, including objectives and tasks.

Homework Sets

1. Hilbert Transform and Fourier Analysis

Objectives:

• Compute the Hilbert Transform of given signals.
• Analyze and plot the real and imaginary parts of the Hilbert Transforms.
• Compute and plot the Fourier Transform of the given signals.
• Compare results obtained through manual calculations and MATLAB built-in functions.

Tasks:

1. Compute the Hilbert Transform of the signal ( m(t) ) and plot the results.
2. Use MATLAB functions to compute the Hilbert Transform and verify previous results.
3. Derive and plot the analytic signal corresponding to ( m(t) ).
4. Compute and plot the Fourier Transform of ( m(t) ), and compare with results from FFT.

2. Amplitude Modulation (AM)

Objectives:

• Analyze an amplitude-modulated signal in the time and frequency domains.
• Understand and compute the signal bandwidth and perform sampling.

Tasks:

1. Generate and plot the given AM signal in the time and frequency domains.
2. Determine the bandwidth of the signal and perform appropriate sampling.
3. Modulate the signal using AM and plot the modulated signal and its spectrum.
4. Implement and analyze demodulation techniques, including comparison with MATLAB’s built-in functions.

3. Frequency Modulation (FM)

Objectives:

• Modulate and demodulate signals using frequency modulation.
• Analyze the effect of noise and calculate signal bandwidth.

Tasks:

1. Compute and plot the integral of the signal ( x(t) ).
2. Implement and plot the FM modulated signal using manual calculations.
3. Use MATLAB's built-in FM functions and compare results.
4. Calculate and plot the frequency spectrum of the modulated signal.
5. Use Carson's Rule to determine the bandwidth of the FM signal.
6. Design and analyze a frequency demodulator system and its performance.

4. BPSK Digital Modulation

Objectives:

• Implement and analyze Binary Phase Shift Keying (BPSK) modulation.
• Study the effect of noise and determine the Bit Error Rate (BER).

Tasks:

1. Generate a random binary sequence and plot the BPSK modulated signal.
2. Add white noise to the signal and analyze its effect on transmission.
3. Implement a matched filter and evaluate its performance.
4. Determine the threshold for bit detection to minimize errors.
5. Analyze the Bit Error Rate (BER) for different signal-to-noise ratios (SNR).
6. Plot and compare the BER performance with theoretical results.
7. Investigate the impact of frequency offset on the signal and threshold detection.