Deriving the Convolution Kernel of the Inverse of a Signal

1. What is the inverse of convolution?
2. Why is the kernel reversed in convolution?
3. Do we need to flip the kernel in convolution?
4. What is convolution of signals?

What is the inverse of convolution?

Computing the inverse of the convolution operation is known as deconvolution.

Why is the kernel reversed in convolution?

Basically it's because time goes along the x axis with the small time values on the left and the big (later) time values on the right. So if you start shifting in, you're having the big time values hit your signal first, which is not right (causal). So you have to flip it to make the small time values shift in first.

Do we need to flip the kernel in convolution?

When performing the convolution, you want the kernel to be flipped with respect to the axis along which you're performing the convolution because if you don't, you end up computing a correlation of a signal with itself.

What is convolution of signals?

Convolution is a mathematical way of combining two signals to form a third signal. It is the single most important technique in Digital Signal Processing. Using the strategy of impulse decomposition, systems are described by a signal called the impulse response.