create a function that performs lowpass filtering on 1-d timeseries data expressed as t and x, and accepts a 3rd argument of frequency cutoff in matlab

You can create a MATLAB function that performs lowpass filtering on a 1-D time series data using the filter function in MATLAB's Signal Processing Toolbox. Here's an example of how you can do it:

main.m
function filtered_data = lowpass_filter(t, x, cutoff_freq)
    % t: time vector
    % x: input data
    % cutoff_freq: frequency cutoff in Hz
    
    % Sampling frequency
    fs = 1 / (t(2) - t(1));
    
    % Design the lowpass filter
    % You can choose different filter designs based on your requirements
    filter_order = 10; % Order of the filter (you can adjust this)
    butterworth_filter = designfilt('lowpass', 'FilterOrder', filter_order, 'CutoffFrequency', cutoff_freq, 'SampleRate', fs);
    
    % Apply the filter to the input data
    filtered_data = filter(butterworth_filter, x);
end
605 chars
17 lines

In this function, we calculate the sampling frequency fs based on the time vector t. Then, we design a Butterworth lowpass filter using the designfilt function from the Signal Processing Toolbox. The cutoff_freq argument specifies the cutoff frequency of the filter in Hz.

Finally, we use the filter function to apply the designed filter to the input data x. The filtered data is returned as the output of the function.

Make sure you have the Signal Processing Toolbox installed in MATLAB in order to use the functions designfilt and filter.