Planet Transit Detection System 🌌

Signals and Systems Term Project - 5th Semester

This project demonstrates a modular pipeline developed in MATLAB to detect exoplanetary transits using the transit photometry method. The system simulates the light curve of a distant star and extracts the planet's orbital characteristics from noisy time-series data using periodic correlation.

📡 Signals and Systems Concepts

This project applies fundamental engineering principles to astrophysical "curve light signals":

• Signal Detrending: Utilizing polynomial fitting to remove low-frequency "drift" from non-stationary signals. This acts as a High-Pass Filter operation to level the baseline.
• Time-Domain Filtering: Applying Savitzky-Golay filters to suppress high-frequency white noise. This is preferred over standard moving averages because it preserves the sharp "Ingress" and "Egress" points (edges) of the transit.
• Correlation & Periodicity: Implementing the Box Least Squares (BLS) algorithm, which acts as a Matched Filter. It correlates the data with a square-wave template to find periodic rectangular pulses.
• System Characterization: Mapping the "Output Signal" (flux) back to the "Input System" (orbital mechanics and planetary physics).

🛠️ System Architecture

The pipeline follows a modular architecture to ensure signal integrity:

1. Normalization: Raw flux is converted into a relative scale centered at 1.0 to easily identify small transit dips.
2. Conditioning: The signal is processed through detrending and Savitzky-Golay smoothing to remove stellar noise and sensor drift.
3. Discovery (BLS Engine): A Modulo Operation (Phase Folding) wraps the time-series data onto itself. If the period is correct, signals add constructively (Coherent Integration).
4. Characterization: Signal depth and period are converted into physical units like Planet Radius and Astronomical Units (AU).

📐 Mathematical Foundation

The system utilizes three primary formulas for characterization:

• Transit Depth ($\delta$): $\delta = \frac{\Delta Flux}{Flux_{baseline}} = (\frac{R_{planet}}{R_{star}})^{2}$
• Kepler's Third Law: $a = \sqrt[3]{\frac{GM_{star}P^{2}}{4\pi^{2}}}$
• Signal-to-Noise Ratio (SNR): $SNR = \frac{\delta}{\sigma}\sqrt{N_{transits}}$

💻 Usage

1. Open the project in MATLAB (Signal Processing Toolbox required).
2. Run the main function: ExoplanetDetectionSystem.
3. Use the "Generate Test Data" button to simulate a known planet like WASP-12b to verify the system's accuracy.
4. Analyze the Periodogram for the power spike at the detected period.

👥 Authors (FCSE)

• Hassan Khalid
• Saad Mirza
• Moiz Kakakhel

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Supervised by: Sir Zaheer
Course Instructor: Dr. Hanif