A C Program to Find Convolution of Two Signals

The convolution of ƒ and g is written ƒg, using an asterisk or star. It is defined as the integral of the product of the two functions after one is reversed and shifted. As such, it is a particular kind of integral transform:

(f * g )(t)\ \ \, \stackrel{\mathrm{def}}{=}\ \int_{-\infty}^{\infty} f(\tau)\, g(t - \tau)\, d\tau
= \int_{-\infty}^{\infty} f(t-\tau)\, g(\tau)\, d\tau.       (commutativity)

While the symbol t is used above, it need not represent the time domain. But in that context, the convolution formula can be described as a weighted average of the function ƒ(τ) at the moment t where the weighting is given by g(−τ) simply shifted by amount t. As t changes, the weighting function emphasizes different parts of the input function.

More generally, if f and g are complex-valued functions on Rd, then their convolution may be defined as the integral:

(f * g )(x) = \int_{\mathbf{R}^d} f(y)g(x-y)\,dy = \int_{\mathbf{R}^d} f(x-y)g(y)\,dy.
In Digital Signal Processing where convolution is done between two discrete signals the procedure followed is :
There are different methods used in finding convolution (refer Signals And Systems by  Openheim for more details on each method). Here i will demonstrate a C program that uses the matrix method to find convolution.
/* Vineeth Kartha
Program To Find Convolution
Released Under GPL */
int main()
printf(“\n\tThis program finds the convolution of a signal and its Impulse response\n”);
int i,j,k,x[10],h[10],y[10],a[10][10],n,m;
printf(“enter the number of elements in x[n]:\t”);
printf(“enter the elements of x[n]:\n”);
printf(“enter the number of elements in h[n]:\t”);
printf(“enter the elements of h[n]:\n”);
printf(“%d “,x[i]);
printf(“%d “,h[i]);
printf(“%d “,y[i]);
return 0;

8 thoughts on “A C Program to Find Convolution of Two Signals

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