Inverse Convolution Calculator - Calculator Academy

Enter the original signal, deconvolved signal, and kernel into the calculator to determine the missing variable in the inverse convolution process.

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Inverse Convolution Formula

The following formula is used to calculate the missing variable in the inverse convolution process.

O = D * K

Variables:

O is the original signal
D is the deconvolved signal
K is the kernel

To calculate the original signal, multiply the deconvolved signal by the kernel. Alternatively, you can rearrange the formula to solve for the deconvolved signal or the kernel if the other two variables are known.

What is Inverse Convolution?

Inverse convolution is a mathematical process used to retrieve the original signal from a convolved signal. Convolution is a fundamental operation in signal processing that combines two signals to form a third signal. Inverse convolution aims to reverse this process by deconvolving the signal with a known kernel to recover the original signal. This technique is widely used in various fields such as image processing, audio processing, and communications to remove distortions and recover the original information.

How to Calculate Inverse Convolution?

The following steps outline how to calculate the inverse convolution.

First, determine the deconvolved signal (D).
Next, determine the kernel (K).
Finally, calculate the original signal (O) using the formula O = D * K.
If you have the original signal and the kernel, you can calculate the deconvolved signal using D = O / K.
If you have the original signal and the deconvolved signal, you can calculate the kernel using K = O / D.
After inserting the values and calculating the result, check your answer with the calculator above.

Example Problem :

Use the following variables as an example problem to test your knowledge.

Deconvolved Signal (D) = 5

Kernel (K) = 3

Original Signal (O) = 15