Question #200611

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

π₯(π)={3 β2 1 4} and β(π)={2 5 3}

β β

Expert's answer

π₯(π)={3 β2 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}

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