# Time Domain Analysis Viva Questions

## Time Domain Analysis Viva Questions

Time Domain Analysis Viva Questions, Viva Questions on Time Domain Analysis, Short Questions on Time Domain Analysis, Time Domain Analysis of Continuous-Time Systems Viva Questions, Time Domain Analysis of Discrete-Time Systems Viva Questions, Signal & Systems Short Questions, Engineering Viva Questions

Viva Questions on Systems

Viva Questions on Signals

Q.1. How you can represent an arbitrary input signal x(t) as a linear combination of scaled and shifted unit impulse functions?

Ans. An arbitrary input signal x(t) can be represented as a linear combination of scaled and shifted unit impulse functions given by

x(t)=\int_{-\infty }^{\infty }x(\tau )\delta (t-\tau )d\tau

Q.2. What is convolution integral?

Ans. The output y(t) of a system can be obtained using convolution integral if the input to the system x(t) and impulse response of the system h(t) is known. The convolution integral is given by

y(t)=\int_{-\infty }^{\infty }x(\tau )h (t-\tau )d\tau

Q.3. State the distributive property of convolution.

Ans. The distribution property of convolution is given by

x_{1}(t)\ast [x_{2}(t)+x_{3}(t)]=x_{1}(t)\ast x_{2}(t)+x_{1}(t)\ast x_{3}(t)

Q.4. State the commutative property of convolution.

Ans. The commutative property of convolution is given by

x_{1}(t)\ast x_{2}(t)=x_{2}(t)\ast x_{1}(t)

Q.5. State the associative property of convolution.

Ans. The associative property of convolution is given by

x_{1}(t)\ast [x_{2}(t)\ast x_{3}(t)]=[x_{1}(t)\ast x_{2}(t)]\ast x_{3}(t)

Q.6. What is the condition for a system to be causal?

Ans. An LTI continuous system is causal if and only if its impulse response is zero for negative values of t.

Q.7. What is the necessary and sufficient condition on the impulse response for stability?

Ans. The necessary and sufficient condition for an LTIC system to be stable is that the impulse response of the system is absolutely integrable. That is

\int_{-\infty }^{\infty }\left|h(t) \right|< \infty

Q.8. Give four steps to compute the convolution integral.

Ans.

1. Graph the signals x(τ) and h(τ) as a function of independent variable τ.
2. Obtain the signal h(t – τ) by folding h(τ) about τ = 0 and then time shifting by time t.
3. Graph both signals x(τ) and h(t – τ) on the same τ -axis beginning with very large negative time shift t.
4. Multiply the two signals x(τ) and h(t – τ) and integrate over the over-lapping interval of two signals to obtain y(t).
5. Increase the time shift t and take the new interval whenever the function of either x(τ) and h(t – τ) changes, and calculate y(t) for this new interval using step 4.
6. Repeat step 5 and 4 for all intervals.

Q.9. What is the overall impulse response h(t) when two systems whose impulse responses h1 (t) and h2 (t) are in parallel and in series?

Ans. If the two systems whose impulse responses h1 (t) and h2 (t) are in parallel, then the overall impulse response is

h(t)=h_{1}(t)+ <span style="mso-spacerun:yes"> </span>h_{2}(t)

If the two systems are connected in series, then the overall impulse response is

h(t)=h_{1}(t)\ast h_{2}(t)

Q.10. Define the terms (i) Natural response (ii) Forced response.

Ans.

• Natural response: It is the response of the system with zero input. It depends on the initial state of the system.
• Forced response: It is the response of the system due to input alone when the initial state of the system is zero.

Q.11. Define the impulse response and step response of a system.

Ans. The impulse response of a system is the output of the system when the input signal is an impulse function. The step response of a system is the output of the system when the input signal is a unit step function.

Q.12. What is meant by discrete convolution?

Ans. The convolution of discrete-time signals is known as discrete convolution. Let x(n) be the input to an LTI system and y(n) be the output of the system. If h(n) is the impulse response h(n) of the system, then the output y(n) can be obtained by convoluting the impulse response h(n) and the input signal x(n).

y(n)=\sum_{k=-\infty }^{\infty }x(k)h(n-k)

Or

y(n)=\sum_{k=-\infty }^{\infty }h(k)x(n-k)

Q.12. What are the properties of convolution?

Ans.

1. Commutative Property: x(n)\ast h(n)=h(n)\ast x(n)
2. Associative Property: [x(n)\ast h_{1}(n)]\ast h_{2}(n)=x(n)\ast[ h_{1}(n)\ast h_{2}(n)]
3. Distribute Property: x(n)\ast[ h_{1}(n)+ h_{2}(n)]=x(n)\ast h_{1}(n)+ x(n)\ast h_{2}(n)

Q.13. What are FIR and IIR systems?

Ans. FIR system: The FIR system has an impulse response that is zero outside a finite time interval. Example: h(n) = 0 for n < 0 and n ≥ N

IIR system: An IIR system exhibits an impulse response of infinite duration.

Q.14. Define a stable and causal system.

Ans.

Stable system: Any relaxed system is said to be bounded input bounded output (BIBO) stable if and only if every bounded input yields a bounded output.

Causal system: A system is said to be causal if the output of the system at any time n depends only on present and past input, but does not depend on future inputs.

Q.15. What is causality condition for an LTI discrete-time system?

Ans. The necessary and sufficient condition for causality of an LTI system is its, unit sample response h(n) = 0 for negative values of n, i,e., h(n) = 0 for n < 0

Q.16. What is the necessary and sufficient condition on the impulse response for stability?

Ans. The necessary and sufficient condition guranteeing the stability of a linear time-invariant system is that its impulse response is absolutely summable.

i.e., \sum_{k=-\infty }^{\infty }\left|h(k) \right|< \infty

Q.17. What is the overall impulse response h(n) when two systems with impulse response h1(n) and h2(n) are connected in parallel and in series?

Ans. For series connection of systems h(n)=h_{1}(n)\ast h_{2}(n)

For parallel connection of systems h(n)=h_{1}(n)+ h_{2}(n)

Q.18. Find the linear convolution of x(n) = {1,2,3,4,5,6} with y(n) = {2,-4,6,-8}

Figure 13

x(n)\ast y(n)=\left\{2, 0, 4, 0, -4, -8, -26, -4, -48 \right\}