Question

Find the regular convolution of the following sequences using tabular method:

𝑥(𝑛)={3 −2 1 4} and ℎ(𝑛)={2 5 3}

↑ ↑

Answer 1

𝑥(𝑛)={3 −2 1 4}

Range of $x(n)=-3 \eqslantless n\eqslantless0$

$\therefore x[-n]=$ {-4 +2 -3 -1}

Range of $x(-n)=3 \eqslantless n\eqslantless0$

Conolution of x[n] and x[-n] $=y[x]=x[n] \text{\textcircled * x[-n]}$

The range of elements of y[n] will be $y[n] \varepsilon -3\eqslantless n \eqslantless3$

Hence elements can be calculated from -3 to 3 by summing up diagonals

y[-3]=4

y[-2]=12+-2=10

y[-1]= -8+-6+3=-11

y[0]=16+4+9+1=30

y[1]=-8+-6+3=-11

y[2]=12+-2=10

y[3]=4

y[n]={4,10,-11,30,-11,10,4}