How can I structure a loop to calculate a range of residuals to determine optimal filter cut-off frequency?

I'm new to loops and I'd like some help in structuring a for loop statement so I can calculate the root mean square error for a range of different filter cut-off frequencies and store those results in a vector.

This is the design of my filter. However, I'm not certain of how to assign fcutlow to account for a wide range of cut-offs.

% Filter design.
fs = 800 % Sampling frequency.
fcutlow = (4:0.1:20); % Cut-off frequency in Hz. Start at 4 Hz, increment by 0.1 Hz and end at 20 Hz.
order = 4;
[b, a] = butter(order, fcutlow / (fs / 2));

% Filter data.
filt = filtfilt(b, a, rawdata);

I essentially want to run a for loop to repeat the statements above. I'm just stuck on how to structure my for loop so I can calculate the root mean square error between the filtered data (filt) and rawdata for a cut-off starting at 4 Hz, incrementing by 0.1 Hz and ending at 20 Hz. My residual calculation is:

rmse = sqrt(mean((rawdata - filt) .^2));

I then want the rmse of every iteration stored in a separate vector so I can plot them later.

Can someone please help me structure these statements in a for loop?

Thank you.

Answer 1

[Ahmed Redissi]

Hi,

You can structure your loop this way to iterate over the cutoff frequencies and calculate the root mean square error:

fcutlow = (4:0.1:20); % Cut-off frequency in Hz. Start at 4 Hz, increment by 0.1 Hz and end at 20 Hz.
N = numel(fcutlow); % Number of cut-off frequencies
rmse = zeros(1,N); % Initialize the RMSE array to zeros
fs = 800; % Sampling frequency.
order = 4;
for i = 1:N
    % Filter design.
    [b, a] = butter(order,fcutlow(i)/(fs/2));

    % Filter data.
    filt = filtfilt(b,a,rawdata);
    
    % Calculate the RMSE
    rmse(i) = sqrt(mean((rawdata-filt) .^2));
end

% Plot the RMSE versus the cut-off frequency
plot(fcutlow,rmse)
xlabel('Cut-off Frequency (Hz)')
ylabel('RMSE')

[Benjamin Horsley]

Thank you, @Ahmed Redissi.

[Ahmed Redissi]

You're welcome