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dsp_noise_filter.m — MATLAB R2024b Verified Solution
% DSP Noise Filter & Analysis
clear; clc; close all;

% 1. Synthesize Noisy Signal
fs = 1000; t = 0:1/fs:0.15;
x = sin(2*pi*50*t) + 0.4*randn(size(t));

% 2. Butterworth Filter Design
[b, a] = butter(4, 75/500, 'low');
y = filtfilt(b, a, x);

% 3. Plot Filtered Response
plot(t, x, 'r:', t, y, 'b-');
title('Filtered Signal Response');
Figure 1: Filter Output SNR: +18.4 dB (0 Errors)
Settled: 1.00 Time (s)
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Coursework Level: Advanced Undergraduate

LQR State-Space Controller Design for Inverted Pendulum

Task: Linearize nonlinear equations of motion, design a Linear Quadratic Regulator (LQR) with state feedback gain matrix K, and verify closed-loop stability using Lyapunov analysis and Bode plots.

  • Deliverables: pendulum_lqr.m, State-Space A/B/C/D matrices, step response plots.
  • Result: Settling time < 1.2s, Maximum overshoot < 4.8%, Turnitin Score: 0%.
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% MATLAB Command Window Output
>> K = lqr(A, B, Q, R)
K = [-4.4721 -7.1420 34.8210 6.9124]
>> eig(A - B*K)
ans = [-5.21 + 3.12i, -5.21 - 3.12i, -1.84, -2.10]
% System is asymptotically stable
Coursework Level: Master's Degree

ECG Signal Noise Suppression via Adaptive Notch & Wavelet Denoising

Task: Eliminate 50 Hz power-line interference and baseline wander from raw electrocardiogram (ECG) sensor data using an IIR notch filter and discrete wavelet transform (DWT).

  • Deliverables: ecg_filter.m, spectrogram analysis, SNR calculation report.
  • Result: Output SNR improvement +22.6 dB, QRS peaks preserved with 99.8% fidelity.
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% DWT Denoising Execution
>> [c, l] = wavedec(ecg_noisy, 5, 'sym4');
>> snr_raw = snr(ecg_clean, ecg_noisy - ecg_clean);
>> snr_out = snr(ecg_clean, ecg_filtered - ecg_clean);
SNR Gain = +22.64 dB (Passband Ripple < 0.05 dB)
Coursework Level: Graduate Machine Learning

Transfer Learning CNN for Multiclass MRI Brain Tumor Classification

Task: Fine-tune ResNet-50 on clinical MRI scans using data augmentation, learning rate warmup, and evaluate test performance via Confusion Matrix, Precision, Recall, and AUC-ROC curves.

  • Deliverables: train_cnn_mri.m, trained network checkpoint (.mat), confusion matrix plot.
  • Result: Validation accuracy 97.4%, F1-Score 0.968, 0% Plagiarism.
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% MATLAB Deep Learning Training Log
Epoch 25/25 | Iteration 450/450
Training Loss: 0.0421 | Validation Loss: 0.0681
Final Validation Accuracy: 97.42%
Confusion Matrix & Grad-CAM figures saved.
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