Fourier-Analysis-Exploration

Project Overview

This project focuses on Fourier analysis, sampling, reconstruction, and aliasing in signal processing using MATLAB. It consists of two main components:

1. Fourier Analysis: Implementation of Fourier Series and Fourier Transform.
2. Sampling and Reconstruction: Investigating the effects of different sampling rates and reconstructing signals.

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Project Structure

EECE340_Project/
│── 1_FourierAnalysis/
│   │── ffs.m              # Fourier Series Implementation
│   │── ftr.m              # Fourier Transform Implementation
│   │── iftr.m             # Inverse Fourier Transform
│   │── main1.m            # Main script for Fourier Analysis
│
│── 2_SamplingReconstruction/
│   │── sample.m           # Sampling function
│   │── reconstruct.m      # Signal Reconstruction function
│   │── main_samp_rec.m    # Main script for sampling & reconstruction
│   │── main_Real.m        # Real-world application testing
│   │── 19_R.csv           # Sampled data (Right)
│   │── 25_L.csv           # Sampled data (Left)
│   │── 27_B.csv           # Sampled data (Blink)

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Running the Project

1. Fourier Analysis

To analyze Fourier representations, execute:

main1;

This will:

• Compute and plot Fourier Series approximations.
• Compute and plot Fourier Transform results.
• Perform error analysis based on different parameters.

2. Sampling and Reconstruction

To investigate sampling effects and reconstruct signals, execute:

main_samp_rec;

This will:

• Sample signals at different rates (0.5fN, 2fN, and 4*fN).
• Reconstruct signals and compare results.

3. Real-world Signal Processing

To process real-world eye movement data (Blink, Left, Right), execute:

main_Real;

This will:

• Read sampled data from CSV files.
• Apply sampling and reconstruction.
• Plot the results for different conditions.

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Function Descriptions

1. Fourier Analysis

• ffs.m: Computes the Fourier Series approximation of a signal.
• ftr.m: Computes the Fourier Transform of a signal.
• iftr.m: Computes the Inverse Fourier Transform.

2. Sampling & Reconstruction

• sample.m: Samples a signal at a given rate.
• reconstruct.m: Reconstructs a signal using sinc interpolation.
• main_samp_rec.m: Compares sampling and reconstruction at different rates.
• main_Real.m: Processes real-world signals and applies sampling and reconstruction.

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Notes

• Ensure all .csv files are in the same directory as main_Real.m.
• MATLAB's built-in functions for Fourier analysis are not used to ensure manual implementation.
• Modify sampling rates in main_samp_rec.m as needed for further experimentation.

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Contributors

This project was completed by Lynn Ariss, Raghad Al Agha and Claritta Khoury as part of the EECE 340 course at the American University of Beirut.