Question

What is the convolution of x[n]=^e-n2 and h[n]=n^2?

(a) 5.318n^2 + .123

(b) 6.318n^2 + .123

(c) 5.318n+.88

(d) 5.318n^2+.8846

The question was posed to me in an interview for job.

The doubt is from Discrete Time Convolution topic in section Time-Domain Analysis of CT Systems of Signals and Systems

Answer 1

Right answer is (d) 5.318n^2+.8846

The explanation is: x[n]*h[n]=∑x[k]h[n-k]

=∑e^-k2[(n-k)^2]

=3n^2∑e^-k2 + ∑k^2  e^-k2

=5.318n^2+.8846.