## Instructions

**Objective**

## 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.