125 – PART A ONLY .

Please complete Part A of the Digital Signal Processing (ELEC 30001.3) assignment fully and correctly using MATLAB.

The assignment is based on the simulation and analysis of a seismic P-wave signal contaminated by environmental noise, followed by FIR filter design and frequency-domain analysis.

Requirements:

1. Generate a sinusoidal signal representing a seismic P-wave with:
   • Frequency = 2.3 Hz
   • Sampling Frequency = 100 Hz
   • Duration = 5 seconds
2. Plot the generated signal in the time domain with:
   • Proper title
   • X-axis label (Time in seconds)
   • Y-axis label (Amplitude)
   • Grid enabled
3. Generate broadband colored noise centered at 8 Hz to represent environmental interference.
4. Add the noise to the original signal to create a noisy signal.
5. Design an FIR Low-Pass Filter using:
   • Hamming window
   • Appropriate filter order (recommended 5060)
   • Cutoff frequency around 4 Hz
6. Apply the FIR filter to the noisy signal using MATLAB DSP functions such as:
   • fir1
   • filter or filtfilt
7. Plot the following using subplots:
   • Noisy signal
   • Filtered signal
8. Compute the FFT of:
   • Original signal
   • Noisy signal
9. Plot the following spectra over the frequency range 0 to Fs/2:
   • Magnitude Spectrum
   • Phase Spectrum
10. Provide a critical comparison discussing:
    • Spectral characteristics before and after adding noise
    • How the 8 Hz noise affects identification of the 2.3 Hz seismic component
11. Evaluate the FIR filter performance, including:
    • Justification for selecting an FIR filter
    • Reason for choosing the Hamming window
    • Reason for the chosen filter order
    • Trade-off between transition bandwidth and computational complexity
    • Suitability for real-time seismic monitoring
12. Write clear explanations for every step.
13. Include all generated figures in the report.
14. Comment the MATLAB code thoroughly.
15. Ensure all plots are properly scaled and labelled.
16. Prepare and submit the following files:
    • MATLAB script file (.m)
    • MATLAB figure files if generated (.fig)
    • Word report containing explanations, code snippets, plots, results, and discussion
    • Presentatio
17. Format the report according to the assignment requirements:
    • Times New Roman, size 12
    • Headings in size 14, bold, uppercase, and underlined
    • Title page
    • Table of Contents
    • References in APA 7th edition
18. Ensure the work is original and ready for viva/presentation.

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