Question

how to convolution of two signals...?

Answer 1

If you have two signals, f and g, their convolution is
\[ (f\star g)(t) = \int dx \space f(x) \cdot g(t - x) \]

Answer 2

You can also take the Fourier transform of each signal, multiply them then find the inverse Fourier of the result. Sometimes this is easier than calculating convolution directly.

Answer 3

fourier transform is very nice tool but there some other tool to get convolution faster way and easly

Answer 4

Here's a direct way for discrete convolutions:

$$
x[n]=[x_0,x_1]\\
y[n]=[y_0,y_1,y_2]\\
h[n]=x[n]\star y[n]=\\
\begin{matrix}
&0&x_1&x_0\\
\times& y_0&y_1&y_2\\
\end{matrix}\\
~~~~~~-----\\
~~~~~~~h[2]~h[1]~h[0]\\
\implies h[n]=\{h[0],h[1],h[2]\}
$$
For example:
$$

This is one of the easiest ways I know.

Hope this helps.
x[n]=[1,2]\\
y[n]=[3,4,5]\\
h[n]=x[n]\star y[n]=\\
\begin{matrix}
&&&0&2&1\\
\times&&& 3&4&5\\
\end{matrix}\\
~~~~~~~~~~~-----\\
\begin{matrix}
&&0&10&5\\
&0& 8&4&\\
0&6& 3&&\\
\end{matrix}\\
--------\\
0\quad6\quad11\quad14\quad5\\
\implies h[n]=[5,14,11,6]
$$

Answer 5

Suppose g[x]=a[x]*b[x];

g[x]=\[\sum_{n=-\infty}^{\infty}a[x]b[x-n]\]