how to low pass filter data to remove high-frequency content from the original signal in matlab

To low pass filter data in MATLAB, you can use the built-in lowpass function. This function designs a FIR (finite impulse response) filter that passes low frequency signals and attenuates high frequency signals.

Here's an example code that demonstrates how to use lowpass function to filter a noisy signal x:

main.m
fs = 1000; % Sampling frequency (in Hz)
fc = 100; % Cutoff frequency (in Hz)
order = 8; % Filter order

% Generate noisy signal
t = 0:1/fs:1-1/fs;
x = sin(2*pi*50*t) + sin(2*pi*120*t) + 0.5*randn(size(t));

% Design low pass filter
[b, a] = butter(order, fc/(fs/2), 'low'); % First-order Butterworth filter

% Apply filter to signal
y = filter(b, a, x);

% Plot original and filtered signals
subplot(2,1,1)
plot(t, x)
title('Original signal')
xlabel('Time (s)')
ylabel('Amplitude')

subplot(2,1,2)
plot(t, y)
title('Filtered signal')
xlabel('Time (s)')
ylabel('Amplitude')
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In this example, we first defined the sampling frequency fs, cutoff frequency fc, and filter order order. Then, we generated a noisy signal x that consists of two sine waves with frequencies of 50 Hz and 120 Hz, plus gaussian noise. Next, we designed a Butterworth low pass filter using butter function with the specified cutoff frequency and order. Finally, we applied the filter to the signal using filter function, and plotted the original and filtered signals using subplot and plot functions.

Note that in this example we used a Butterworth filter, but you can also use other types of filters such as Chebyshev and Elliptic filters by using their respective functions (cheby1, cheby2, ellip).