Reconstruct original signal from filtered one with filter coefficients

Hello everyone,

I would like to know if there is a method to reconstruct an original signal from a filtered one with filter coefficients.

For example, X is my original signal and is filtered by a low pass filter with coefficients [b,a]. The output is Y.

So how to get X back from Y and [b,a]?

Thank you for your answer

Answer 1

[Ashutosh Thakur]

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)

X_reconstructed = 1x5

1 2 3 4 5

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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!