Confusions regarding convolution?

1. What is the main purpose of convolution?
2. How do you define convolution *?
3. What is convolution theorem in DSP?

What is the main purpose of convolution?

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.

How do you define convolution *?

Explanation: Convolution is defined as weighted superposition of time shifted responses where the whole of the signals is taken into account. But multiplication leads to loss of those signals which are after the limits.

What is convolution theorem in DSP?

The convolution theorem (together with related theorems) is one of the most important results of Fourier theory which is that the convolution of two functions in real space is the same as the product of their respective Fourier transforms in Fourier space, i.e. f ( r ) ⊗ ⊗ g ( r ) ⇔ F ( k ) G ( k ) .