What do you mean by linear convolution?

Hereâs a brief overview:

1. **Definition**: Convolution involves two functions \( f(t) \) and \( g(t) \). The result of the convolution is a new function \( h(t) \) which is defined as the integral of the product of \( f \) and a shifted version of \( g \).

For continuous functions, the convolution is given by:

\[

(f * g)(t) = \int_{-\infty}^{\infty} f(\tau) \cdot g(t - \tau) \, d\tau

\]

For discrete sequences, itâs given by:

\[

(f * g)[n] = \sum_{m=-\infty}^{\infty} f[m] \cdot g[n - m]

\]

2. **Application**: In signal processing, convolution is used to filter signals, apply effects, and analyze systems. For instance, in image processing, convolution can be used to apply blurring, sharpening, or edge-detection effects to an image.

3. **Properties**: Convolution has several important properties, including commutativity, associativity, and distributivity. These properties make it a powerful tool in various fields of engineering and mathematics.

In simple terms, linear convolution combines two inputs to produce an output that reflects how one input (the filter or system response) modifies the other input (the signal or data).