Signals & Systems Questions and Answers Part-20

1. If h1, h2 and h3 are cascaded, find the overall impulse response
a) h1 * h2 * h3
b) h1 + h2 + h3
c) h3
d) all of the mentioned

Answer: a
Explanation: The resultant impulse response will be the convolution of all the subsequent impulse responses.

2. Find the value of [d(t-3) – d(t-1)] * x[t+3].
a) x(t+3) – x(t+2)
b) x(t) – x(t+1)
c) x(t) – x(t+2)
d) x(t-1) – x(t+2)

Answer: c
Explanation:The delta function convolved with another function results in the shifted function.

3. If h1, h2 and h3 are cascaded, and h1 = u(t), h2 = d(t) and h3 = d(t), find the overall impulse response
a) s(t)
b) d(t)
c) u(t)
d) all of the mentioned

Answer: c
Explanation: The resultant impulse response will be the convolution of all the subsequent impulse responses.

4. If h1, h2 and h3 are cascaded, and h1 = u(t+4), h2 = d(t-3) and h3 = d(t-5), find the overall impulse response
a) u(t-4)
b) u(t-6)
c) u(t-8)
d) all of the mentioned

Answer: a
Explanation: The resultant impulse response will be the convolution of all the subsequent impulse responses.

5. Find the value of [u(t) – d(t-1)] * -x[t+1].
a) $x(t+1) – x(t)
b) x(t) – $x(t+1)
c) $x(t) – x(t-1)
d) $x(t-1) – x(t+1)

Answer: b
Explanation: The delta function convolved with another function results in the shifted function.

6. If h1, h2 and h3 are parallelly summed, find the overall impulse response
a) h1 + h2 + h3
b) h1 – h2 + h3
c) h1*h2*h3
d) all of the mentioned

Answer: a
Explanation: The resultant impulse response will be the convolution of all the subsequent impulse responses.

7. Find the value of [u(t) – u(t+1)] * x[t+1].
a) $x(t+1) – $x(t+3)
b) $x(t) – $x(t+2)
c) $x(t) – $x(t-1)
d) $x(t+1) – $x(t+2)

Answer: d
Explanation: The delta function convolved with another function results in the shifted function.

8. If h1, h2 and h3 are cascaded, and h1 = u(t), h2 = exp(t) and h3 = sin(t), find the overall impulse response
a) sin(t)*exp(t)*u(t)
b) sin(t) + exp(t) + u(t)
c) u(t)*sin(t)
d) all of the mentioned

Answer: a
Explanation: The resultant impulse response will be the convolution of all the subsequent impulse responses.

9. What is periodic convolution?
a) Continuous type superposition
b) Periodic type summation
c) Discrete type addition
d) Summation of both continuous and periodic type

Answer: b
Explanation: When a function g is periodic, with period T, then for functions, f, such that f∗g exists, the convolution is also periodic. This is called a periodic convolution.
Example: f*g=∫∑[f(e+kT)]g(t-e).

10. What is a circular or cyclic convolution?
a) Convolution of a periodic and continuous time function
b) Convolution of a periodic and discrete time function
c) Superposition of periodic and periodic function
d) Summation of continuous time and a convolution of a periodic function convolution

Answer: d
Explanation: The circular convolution is done of two aperiodic functions (i.e. Schwartz functions) happens when one of them is convolved in the normal way with a periodic summation of the other given function.
(Xn*h)[n]=∑h[m].xn[n-m], for discrete sequences n.