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.

Example

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

Visualization

Frequency Domain Analysis

• The basic command to do the Fourier analysis is “fft”,

Time domain and Frequency domain representation

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.

Example

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