# Matlab Program to Filter ECG Signals Assignment Solution

June 11, 2024
Prof. Ryan
🇨🇦 Canada
Programming
Prof. Ryan Jackson, a renowned authority in programming, earned his Ph.D. from the University of Toronto, Canada. With 15 years of expertise, he guides students with precision, drawing from his extensive academic background and industry insights.
Key Topics
• Instructions
• Requirements and Specifications
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## Instructions

Objective

Write a program to filter ECG signals in matlab.

## Requirements and Specifications

Source Code

```clc, clear all, close all %% First, load the signal load ecg_person_1.mat % Store the signal in a variable named 'y' y = ecg_person_1; % Plot signal figure(1) plot(tm, y) xlabel('Time (s)') ylabel('Magnitude') grid on %% Question 2: Get duration of signal % We were told that the signal is recorded with 500 samples per second so % to get the total duration of the signal we just need to divide the total % number of samples by 500 Tf = length(y)/500; fprintf("The signal has a duration of %.2f seconds\n", Tf); %% Question 3: Standard frequency % The standard frequencty of ECG signals can vary between 0.5Hz to 100 or % 150 Hz [1] %% Question 4: Spectral Analysis % let's plot a frequency spectrum analysis to check the main frequency % on the signal and see if there are other frequencies % Frequency spectrum % Time step dt = tm(2)-tm(1); % Sampling frequency Fs = 1/dt; % Fast Fourier Transform Y = fft(ecg_person_1); % Length of signal L = length(ecg_person_1); P2 = abs(Y/L); P1 = P2(1:L/2+1); P1(2:end-1) = 2*P1(2:end-1); f = Fs*(0:(L/2))/L; figure(2) plot(f,P1) title('Single-Sided Amplitude Spectrum of ECG Signal') xlabel('Frequency (Hz)') ylabel('Magnitude') grid on % From the graph, we can see that the main frequency on the signal is 50Hz. % We can also note that the signal has a lot of low-frequencies noise, so % we now know that we need to filter these low frequencies. We can also see % that the signal has frequencies of 150 Hz. This kind of noise is caused % by the muscles when reading the ECG signals, so we will apply a bandpass % filter to keep only the frequencies near 50 Hz %% Question 5: Design a bandpass filter to filter frequencies higher than 100 Hz % First, we remove the trend from the signal. We assume a trend of a 4-th % order polynomial. We assume this because after trial-and-error, this % value returned a signal with the trend removed yf = detrend(y,4); % Now, we remove noise yf = medfilt1(yf, 10); % Now, we remove the low frequencies [yf,d] = bandpass(yf, [20,70], Fs); % Get transfer function % Plot figure(3) plot(tm, y) hold on plot(tm, yf) legend('Original', 'Filtered') xlabel('Time (s)') ylabel('Magnitude') grid on % Frequency spectrum of filteres signal [b,a] = tf(d); H = tf(b,a) % Now, show Frequency Spectrum of the filtered signal % Fft Y = fft(yf); P2 = abs(Y/L); P1 = P2(1:L/2+1); P1(2:end-1) = 2*P1(2:end-1); f = Fs*(0:(L/2))/L; figure(4) plot(f,P1) title('Single-Sided Amplitude Spectrum of Filtered Signal') xlabel('Frequency (Hz)') ylabel('Magnitude') grid on %% References % [1] https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4624499/#:~:text=Modern%20ECG%20machines%20record%20ECG,Hz%20as%20an%20industry%20standard. ```

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