Write a function with the declaration: smoothed=rectFilt(x,width). The filter should take a vector of noisy data (x) and smooth it by doing a symmetric moving average with a window of the specified width. For example if width=5, then smoothed(n) should equal mean(x(n-2:n+2)). Note that you may have problems around the edges: when n<3 and n>length(x)-2. a. The lengths of x and smoothed should be equal. b. For symmetry to work, make sure that width is odd. If it isn’t, increase it by 1 to make it odd and display a warning, but still do the smoothing. c. Make sure you correct edge effects so that the smoothed function doesn’t deviate from the original at the start or the end. Also make sure you don’t have any horizontal offset between the smoothed function and the original (since we’re using a symmetric moving average, the smoothed values should lie on top of the original data). d. You can do this using a loop and mean (which should be easy but may be slow), or more efficiently by using conv (if you are familiar with convolution). e. Load the mat file called noisyData.mat. It contains a variable x which is a noisy line. Plot the noisy data as well as your smoothed version, like below (a width of 11 was used):
时间: 2024-03-10 20:46:21 浏览: 16
Sure, here's the code for the rectFilt function:
```
function smoothed = rectFilt(x, width)
%RECTFILT Smooths a vector of noisy data using a symmetric moving average with a specified window width.
% smoothed = rectFilt(x, width) returns a vector that is the same size as x, where each element in the vector is the
% mean of a symmetric window of width 'width' centered around that element in x.
% Check that width is odd
if mod(width, 2) == 0
warning('Width is even. Increasing by 1 to make it odd.');
width = width + 1;
end
% Add padding to handle edge effects
x_padded = [repmat(x(1), [1, (width-1)/2]), x, repmat(x(end), [1, (width-1)/2])];
% Compute moving average using convolution
weights = ones([1, width])/width;
smoothed = conv(x_padded, weights, 'valid');
% Make sure the smoothed function doesn't deviate from the original at the start or the end
smoothed(1:(width-1)/2) = x(1:(width-1)/2);
smoothed(end-(width-1)/2+1:end) = x(end-(width-1)/2+1:end);
end
```
To use this function on the `noisyData.mat` file and plot the results, you can run the following code:
```
load('noisyData.mat');
% Smooth the data with a width of 11
smoothed = rectFilt(x, 11);
% Plot the original data and the smoothed data
plot(x, 'b');
hold on;
plot(smoothed, 'r');
legend('Original', 'Smoothed');
```
I hope this helps! Let me know if you have any questions.