## Signals & Systems Questions and Answers Part-19

1. Evaluate (exp(-at)u(t))*u(t), u(t) being the heaviside function.
a) (1-exp(at)) u(t)/a
b) (1-exp(at)) u(-t)/a
c) (1-exp(-at)) u(t)/a
d) (1+exp(-at)) u(t)/a

Explanation: Use the convolution formula.

2. Find the value of h[n]*d[n-5], d[n] being the delta function.
a) h[n-2].
b) h[n-5].
c) h[n-4].
d) h[n+5].

Explanation: Convolution of a function with a delta function shifts accordingly.

3. Evaluate (exp(-4t)u(t))*u(t), u(t) being the heaviside function.
a) (1-exp(4t)) u(t)/a
b) (1-exp(-4t)) u(t)/a
c) (1-exp(=4t)) u(t)/a
d) (1+exp(-4t)) u(t)/a

Explanation: Use the convolution formula.

4. Find the value of h[n-1]*d[n-1], d[n] being the delta function.
a) h[n-2].
b) h[n].
c) h[n-1].
d) h[n+1].

Explanation: Convolution of a function with a delta function shifts accordingly.

5. Find the convolution of x(t) = exp(2t)u(-t), and h(t) = u(t-3)
a) 0.5exp(2t-6) u(-t+3) + 0.5u(t-3)
b) 0.5exp(2t-3) u(-t+3) + 0.8u(t-3)
c) 0.5exp(2t-6) u(-t+3) + 0.5u(t-6)
d) 0.5exp(2t-6) u(-t+3) + 0.8u(t-3)

Explanation: Divide it into 2 sectors and apply the convolution formula.

6. Find the value of h[n]*d[n+1], d[n] being the delta function.
a) h[n-2].
b) h[n].
c) h[n-1].
d) h[n+1].

Explanation: Convolution of a function with a delta function shifts accordingly.

7. Find the convolution of x(t) = exp(3t)u(-t), and h(t) = u(t-3)
a) 0.33exp(2t-6) u(-t+3) + 0.5u(t-3)
b) 0.5exp(4t-3) u(-t+3) + 0.8u(t-3)
c) 0.33exp(2t-6) u(-t+3) + 0.5u(t-6)
d) 0.33exp(3t-6) u(-t+3) + 0.33u(t-3)

Explanation: Divide it into 2 sectors and apply the convolution formula.

8. Find the value of d(t-34)*x(t+56), d(t) being the delta function.
a) x(t + 56)
b) x(t + 32)
c) x(t + 22)
d) x(t – 22)

Explanation: Convolution of a function with a delta function shifts accordingly.

9. Find x(t)*u(t)
a) tx(t)
b) t2x(t)
c) $x(t2) d)$x(t)