### Computation of linear convolution

The different method used for the computation of linear convolution is as follows :
• Graphical method
• Using the mathematical equation of convolution
• Tabulation method
• Multiplication method

Graphical method :

y (n)  =  ∑  x (k) h(n-k)
k= -∞

for n = 0

y (0)  =  ∑  x (k) h(-k)
k= -∞

for n =1

y (1)  =  ∑  x (k) h(1-k)
k= -∞

Here the term (1-k) can be written as h(-k+1).

y (1)  =  ∑  x (k) h(-k+1)
k= -∞

Here h(-k+1) indicates of folded signal h(-k). It indicates that h(-k) is delayed by 1 sample. Similarly for other values of n output y (n) is calculated.

Thus different operation involved in the calculation of linear convolution are as follow :
• Folding operation: It indicates folding of sequence h (k)
• Shifting operation: It indicates time shifting of h (-k) e.g h (-k+1)
• Multiplication: It indicates multiplication of x (k) and h (n-k)
• Summation: It indicates the addition of all product terms obtained because of multiplication of x (k) and h (n-k)