How to analyze and process signals: Loading, nature identification, artifact extraction, non-stationarity modeling, synthetic signal generation, and wavelet filtering?

How can I effectively analyze and process a signal using MATLAB, considering the following tasks:

1. Loading a signal from the "signal.mat" file and determining its nature through observations in the time and frequency domains.
2. Identifying any artifacts and/or noise present in the signal and storing them in vectors for later use in simulation.
3. Investigating non-stationarity characteristics of the signal by applying Burg's autoregressive modeling approach to both an initial and a final segment of the recording.
4. Generating a synthetic biopotential signal with the same time-frequency characteristics as one of the previously analyzed segments. Assuming a signal-to-noise ratio (SNR) of 15dB, corrupt the synthetic signal with the extracted artifacts and noise (if available).
5. Applying wavelet filtering to the corrupted synthetic signal and evaluating the filtering quality based on the mean squared error (MSE) parameter.

I need guidance on how to accomplish these tasks effectively using MATLAB.

Answer 1

[Shubh Dhyani]

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,

linspace: https://www.mathworks.com/help/matlab/ref/linspace.html

fft: https://www.mathworks.com/help/matlab/ref/fft.html

fftshift: https://www.mathworks.com/help/matlab/ref/fftshift.html

arburg: https://www.mathworks.com/help/signal/ref/arburg.html

awgn: https://www.mathworks.com/help/comm/ref/awgn.html

wavedec: https://www.mathworks.com/help/wavelet/ref/wavedec.html

waverec: https://www.mathworks.com/help/wavelet/ref/waverec.html