## 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

### Short Questions and Answers

**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

**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

**Q.3.** *State the distributive property of convolution.*

**Ans.** The distribution property of convolution is given by

**Q.4.** *State the commutative property of convolution.*

**Ans.** The commutative property of convolution is given by

**Q.5.** *State the associative property of convolution.*

**Ans.** The associative property of convolution is given by

**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

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

**Ans.**

- Graph the signals
*x(τ)*and*h(τ)*as a function of independent variable τ. - Obtain the signal
*h(t – τ)*by folding*h(τ)*about τ = 0 and then time shifting by time t. - Graph both signals
*x(τ)*and*h(t – τ)*on the same τ -axis beginning with very large negative time shift t. - Multiply the two signals
*x(τ)*and*h(t – τ)*and integrate over the over-lapping interval of two signals to obtain*y(t)*. - 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. - Repeat step 5 and 4 for all intervals.

**Q.9.** *What is the overall impulse response h(t) when two systems whose impulse responses h _{1} (t) and h_{2} (t) are in parallel and in series?*

**Ans.** If the two systems whose impulse responses *h _{1} (t)* and

*h*are in parallel, then the overall impulse response is

_{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.**

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

**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).*

Or

y(n)=\sum_{k=-\infty }^{\infty }h(k)x(n-k)**Q.12.** *What are the properties of convolution?*

**Ans.**

- Commutative Property: x(n)\ast h(n)=h(n)\ast x(n)
- Associative Property: [x(n)\ast h_{1}(n)]\ast h_{2}(n)=x(n)\ast[ h_{1}(n)\ast h_{2}(n)]
- 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 h _{1}(n) and h_{2}(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\}