Hi Tran,
If you want to reconstruct the original signal (X) from the filtered signal (Y), you need to apply an inverse filter to the signal Y. You can apply the inverse filter by switching the coefficients passed to the filter function compared to the original signal. The following lines of sample code will give you more information regarding this approach:
% Original signal
X = [1, 2, 3, 4, 5];
% Filter coefficients
b = [0.5, 0.5];
a = 1;
% Filtered signal
Y = filter(b, a, X);
% Reconstruct the original signal by switching the coefficients
% instead of b,a we will use a,b.
X_reconstructed = filter(a, b, Y)
As you can see, by changing the coefficients from [b, a] to [a, b], we were able to reconstruct the original signal (X) from the filtered one (Y).
You can refer to the following documentation links for more information regarding the filter function in MATLAB:
- https://www.mathworks.com/help/matlab/ref/filter.html.
- https://www.mathworks.com/matlabcentral/answers/338325-inverse-of-filter-function.
I hope this helps you!
