design a butterworth low-pass lter with lter order 20 such that when the signal xptq is applied to this lter, in matlab

To design a Butterworth low-pass filter with a filter order of 20 in MATLAB, use the butter function.

main.m
% Define the filter order
n = 20; 

% Define the cutoff frequency of the filter
fc = 10; 

% Define the sampling frequency
fs = 100; 

% Normalize the cutoff frequency
Wn = fc/(fs/2);

% Use the butter function to design the filter coefficients
[b,a] = butter(n, Wn, 'low');

% Apply the filter to the input signal
y = filter(b, a, xptq);
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Here, n is the filter order, fc is the cutoff frequency, and fs is the sampling frequency in Hz. The Wn variable is the normalized cutoff frequency, which is calculated as the ratio of the cutoff frequency to half the sampling frequency.

The butter function returns the numerator and denominator coefficients of the digital Butterworth filter transfer function for the given filter order and cutoff frequency. The 'low' option in the function call specifies that a low-pass filter should be designed.

Finally, the filter function is used to apply the designed filter coefficients to the input signal xptq, resulting in the filtered output signal y.