design a butterworth low-pass filter with filter order 20 such that when the signal x is applied to this filter, the output does not contain the frequency 330hz in matlab

To design a Butterworth low-pass filter with a filter order of 20 and remove the frequency of 330Hz from the signal x:

main.m
% Define filter specifications
fc = 300; % Cutoff frequency
fs = 1000; % Sampling frequency
Wn = fc/(fs/2); % Normalized cutoff frequency

% Create Butterworth filter
n = 20; % Filter order
[b, a] = butter(n, Wn, 'low');

% Filter signal x
x_filtered = filter(b, a, x); % Removes 330Hz frequency from x
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In the above code, we first define the filter specifications - the cutoff frequency fc and the sampling frequency fs. We then calculate the normalized cutoff frequency Wn.

Using the butter function with the parameters n, Wn and 'low', we create a Butterworth low-pass filter with the desired filter order.

We then apply this filter to the signal x using the filter function. The resulting x_filtered signal will not contain the frequency of 330Hz.