1. Convolution in Matlab
The convolution in matlab is accomplished by using “conv” command.
If “u” is a vector with length ‘n’ and “v” is a vector with length ‘m’, then their convolution will be of length “n+m-1”
Convolution is a commutative operation.
Convolution in time domain corresponds to multiplication in frequency domain.

2. Example

3. The impulse response and input to the system is used to calculate the system output, an example follows

4. Visualization

5. Frequency Domain Analysis
The basic command to do the Fourier analysis is “fft”,

6. Time domain and Frequency domain representation

7. Convolution Using FFT
In frequency domain convolution is merely multiplication of signals, this property is used to find response of systems
Let x1 be an input signal to system with impulse response x2 , we take fft of x1 and x2 and multiply them to get the x3 the frequency domain output from the system.
Ifft(x3) will give us the time domain output.

8. Example

9. Another Example of forming your own functions in matlab
In this example our objective is to form a function which takes x1(input) and x2(impulse response) and returns both the frequency domain and time domain output