Question

Find the convolution of the signals:

𝑥(𝑛)={2 𝑛=−2,0,1

3 𝑛=−1

0 elsewhere}

ℎ(𝑛)=𝛿(𝑛)−2𝛿(𝑛−1)+3𝛿(𝑛−2)−𝛿(𝑛−3)

(a) Graphical method

(b) Sliding strip method

Answer 1

$X[n]= \delta [n]+2\delta [n-1]+3\delta [n-3]+4\delta [n-4]+6\delta [n-6]$

$h[n]= \delta [n+1]+2\delta [n]+\delta [n-1]+\delta [n-2]$

y(n) by circular convolution = [-4,1,6,-3,3,5]