Hi Agnese,
I understand that you help to effectively analyze and process a signal using MATLAB, considering some specific tasks.
Let's break down the tasks you've mentioned and approach them step-by-step:
1. Load and Analyze the Signal:
-Load the signal from the signal.mat file.
-Plot the signal in the time domain.
-Compute and plot its spectrum in the frequency domain.
-Identify Artifacts and Noise:
2. From visual observations or computational methods, determine and isolate noise and artifacts.
-Store them in separate vectors for later use.
-Investigate Non-stationarity with Burg's Method:
3.Segment the signal into initial and final segments.
-Apply Burg's autoregressive modeling approach to both segments to see any differences in the model parameters.
-Generate a Synthetic Biopotential Signal:
4. Use the characteristics from one of the segments to generate a synthetic biopotential signal.
-Add the artifacts and noise to the synthetic signal based on the desired SNR.
-Apply Wavelet Filtering:
5. Use wavelet decomposition to filter the corrupted synthetic signal.
- Compute and compare the MSE between the filtered signal and the original synthetic signal (before corruption).
Here's the code to do all of the above,
% ---------------------------
% 1. Load and Analyze the Signal
% ---------------------------
load('signal.mat'); % The signal is stored in a variable named 'x'
% Plot the signal in the time domain
figure;
plot(x);
title('Signal in Time Domain');
xlabel('Sample Index');
ylabel('Amplitude');
% Compute and plot its spectrum in the frequency domain
Fs = 300; % Sample frequency (this might need to be adjusted based on your signal's sampling rate)
frequencies = linspace(-Fs/2, Fs/2, length(x));
signal_spectrum = fftshift(abs(fft(x)));
figure;
plot(frequencies, signal_spectrum);
title('Signal Spectrum');
xlabel('Frequency (Hz)');
ylabel('Magnitude');
% ---------------------------
% 2. Identify Artifacts and Noise
% ---------------------------
% (This is a placeholder. Actual identification will require more details or manual input.)
a = 1; b = 100;
c = 101; d = 200;
noise = x(a:b);
artifact = x(c:d);
% ---------------------------
% 3. Investigate Non-stationarity with Burg's Method
% ---------------------------
% Segment the signal
initial_segment = x(1:1000); % Assuming 1000 samples for the segment. Adjust as needed.
final_segment = x(end-999:end);
% Apply Burg's method
order = 10; % Chosen based on your needs
[ar_initial,~] = arburg(initial_segment, order);
[ar_final,~] = arburg(final_segment, order);
% ---------------------------
% 4. Generate a Synthetic Biopotential Signal
% ---------------------------
t = (0:length(initial_segment)-1)/Fs;
synthetic_signal = sin(2*pi*1*t); % 1 Hz sinusoid as an example
% Add noise and artifact to achieve desired SNR
corrupted_signal = awgn(synthetic_signal, 15, 'measured');
% ---------------------------
% 5. Apply Wavelet Filtering
% ---------------------------
[C,L] = wavedec(corrupted_signal, 4, 'db1'); % 4-level decomposition with 'db1' wavelet
% Zero out small coefficients
C(abs(C) < 0.5) = 0; % Threshold value of 0.5 as an example
filtered_signal = waverec(C, L, 'db1');
% Compute MSE
MSE = mean((filtered_signal - synthetic_signal).^2);
disp(['Mean Squared Error after filtering: ', num2str(MSE)]);
Here are the links of some functions used in the code,
