## Discrete-Time Signals and Systems Viva Questions

Discrete-Time Signals and Systems Viva Questions, Digital Signal Processing Viva Questions, DSP Viva Questions, Discrete-Time Signals Viva Questions, Discrete-Time Systems Viva Questions, Engineering Viva Questions, Discrete-Time Signals and Systems Viva Questions

*Discrete Convolution and Correlation Viva Questions*

### Short Questions with Answer

**Q.1. ***Define a signal.*

*Ans***. **A signal is defined as a single-valued function of one or more independent variables which contain some information.

**Q.2. ***What is the one-dimensional signal?*

** Ans. **A signal which depends on only one independent variable is called a one-dimensional signal.

**Q.3. ***What is signal modeling?*

** Ans. **The representation of a signal by the mathematical expression is known as signal modeling.

**Q.4. ***What are the different types representing discrete-time signals?*

*Ans***. **There are following four different types of representation of discrete-time signals:

- Graphical representation
- Functional representation
- Tabular representation
- Sequence representation

**Q.5. ***Define unit step sequence.*

*Ans***. **The discrete-time unit step sequence *u*(*n*) is defined as:

**Q.6. ***Define unit ramp sequence.*

*Ans***. **The discrete-time unit ramp sequence *r*(*n*) is defined as:

Or r(n)= nu(n)

**Q.7. ***Define unit parabolic sequence.*

*Ans***. **The discrete-time unit parabolic sequence *p*(*n*) is defined as:

Or p(n)=\frac{n^{2}}{2} u(n)

**Q.8. ***Define unit impulse sequence.*

** Ans. **The discrete-time unit impulse sequence δ(

*n*) is defined as:

**Q.9. ***Write the properties of unit impulse function.*

*Ans***. **The properties of discrete-time unit sample sequence are given as follows:

- \delta (n)=u(n)-u(n-1)
- \delta(n-k)=\left\{\begin{matrix}1, & n=k \\0, & n\neq k \\\end{matrix}\right.
- x(n)=\sum_{\infty }^{k=-\infty }x(k)\delta (n-k)

**Q.10. ***Define a sinusoidal signal.*

*Ans***. **The discrete-time sinusoidal signal is given by

*x*(*n*) = *A *cos (ω_{0}*n +ϕ*)

where ω_{0} is the frequency (in radians/sample), and *ϕ* is the phase (in radians).

**11. ***Define a real exponential signal.*

*Ans***. **The discrete-time real exponential sequence is given by

*x*(*n*) = *a ^{n}u*(

*n*)

where *a *is a constant.

**Q.12. ***Define complex exponential signal.*

*Ans***. **The discrete-time complex exponential signal is given by

where *a *is a constant.

**Q.13. ***What are the basic operations on discrete-time signals?*

*Ans***. **The basic set of operations on discrete-time signals are as follows:

- Time shifting
- Time reversal
- Time scaling
- Amplitude scaling
- Signal addition
- Signal multiplication

**Q.14. ***How are discrete-time signals classified?*

*Ans***. **Discrete-time signals are classified according to their characteristics. Some of them are as follows:

- Deterministic and random signals
- Periodic and aperiodic signals
- Energy and power signals
- Even and odd signals
- Causal and non-causal signals

**Q.15. ***What are digital signals?*

*Ans***. **The signals that are discrete in time and quantized in amplitude are called digital signals.

**Q.16. ***Distinguish between deterministic and random signals.*

*Ans***. **A deterministic signal is a signal exhibiting no uncertainty of its magnitude and phase at any given instant of time. It can be represented by a mathematical equation, whereas a random signal is a signal characterized by uncertainty about its occurrence. It cannot be represented by a mathematical equation.

**Q.17. ***Distinguish between periodic and aperiodic signals.*

*Ans***. **A discrete-time sequence *x*(*n*) is said to be periodic if it satisfies the condition:

*x*(*n*) = *x*(*n *+ *N*) for all *n*

whereas a discrete-time signal *x*(*n*) is said to be aperiodic if the above condition is not satisfied even for one value of *n*.

**Q.18. ***What do you mean by the fundamental period of a signal?*

*Ans***. **The smallest value of *N *that satisfies the condition *x*(*n *+ *N*) = *x*(*n*) for all values of *n *for discrete-time signals is called the fundamental period of the signal *x*(*n*).

**Q.19. ***Are all sinusoidal sequences periodic?*

*Ans***. **In the case of discrete-time signals, not all sinusoidal sequences are periodic.

**Q.20. ***What is the condition to be satisfied for a discrete-time sinusoidal sequence to be periodic?*

** Ans. **For the discrete-time sinusoidal sequence to be periodic, the condition to be satisfied is, that the fundamental frequency ω

_{0}must be a rational multiple of 2π. Otherwise, the discrete-time signal is aperiodic.

**Q.21. ***What is the fundamental period of a discrete-time sinusoidal sequence?*

*Ans***. **The smallest value of positive integer *N*, for some integer *m*, which satisfies the equation *N *= 2π(*m*/ω_{0}) for a sinusoidal periodic signal is called the fundamental period of that signal.

**Q.22. ***Distinguish between energy and power signals.*

*Ans***. **An energy signal is one whose total energy *E *= finite value and whose average power *P *= 0, whereas a power signal is one whose average power *P *= finite value and total energy *E *= ∞.

**Q.23. ***Write the expressions for total energy E and the average power P of a signal.*

** Ans. **The expressions for total energy

*E*and average power

*P*of a signal are:

and

P=\displaystyle \lim_{N \to \infty }\frac{1}{2N}\sum_{n=-N}^{N}\begin{vmatrix} x(n)\end{vmatrix}^{2}for discrete-time signals.

**Q.24. ***Do all the signals belong to either the energy signal or power signal category?*

*Ans***. **No. Some signals may not correspond to either energy signal type or power signal type. Such signals are neither power signals nor energy signals.

**Q.25. ***Distinguish between even and odd signals.*

** Ans. **A discrete-time signal

*x*(

*n*) is said to be an even (symmetric) signal if it satisfies

the condition:

*x*(–*n*) = *x*(*n*) for all *n*

whereas a discrete-time signal *x*(*n*) is said to be an odd (anti-symmetric) signal if it

satisfies the condition:

*x*(–*n*) = – *x*(*n*) for all *n*

**Q.26. ***Do all the signals correspond to either even or odd type?*

*Ans***. **No. All the signals need not necessarily belong to either even or odd type.

There are signals which are neither even nor odd.

**Q.27. ***Can every signal be decomposed into even and odd parts?*

*Ans***. **Yes, every signal can be decomposed into even and odd parts.

**Q.28. ***Write the expressions for even and odd parts of a signal.*

*Ans***. **The even and odd parts of a discrete-time signal are given by

**Q.29. ***Distinguish between causal and non-causal signals.*

*Ans***. **A discrete-time signal *x*(*n*) is said to be causal if *x*(*n*) = 0 for *n *< 0, otherwise the signal is non-causal.

**Q.30. ***Define an anti-causal signal.*

*Ans***. **A discrete-time signal *x*(*n*) is said to be anti-causal if *x*(*n*) = 0 for *n *> 0.

**Q.31. ***Define a system.*

** Ans. **A system is defined as a physical device, which generates a response or output signal for a given input signal.

**Q.32. ***How are discrete-time systems classified?*

** Ans. **The discrete-time systems are classified as follows:

- Static (memoryless) and dynamic (memory) systems
- Causal and non-causal systems
- Linear and non-linear systems
- Time-invariant and time-varying systems
- Stable and unstable systems.
- Invertible and non-invertible systems

**Q.33. ***Define a discrete-time system.*

** Ans. **A discrete-time system is a system that transforms discrete-time input signals into discrete-time output signals.

**Q.34. ***Define a static system.*

** Ans. **A static or memoryless system is a system in which the response at any instant is due to present input alone, i.e. for a static or memoryless system, the output at any instant

*n*depends only on the input applied at that instant

*n*but not on the past or future values of input.

**Q.35. ***Define a dynamic system.*

** Ans. **A dynamic or memory system is a system in which the response at any instant depends upon past or future inputs.

**Q.36. ***Define a causal system.*

** Ans. **A causal (non-anticipative) system is a system whose output at any time

*n*depends only on the present and past values of the input but not on future inputs.

**Q.37. **Define a non-causal system.

** Ans. **A non-causal (anticipative) system is a system whose output at any time

*n*depends on future inputs.

**Q.38. ***What is the homogeneity property?*

** Ans. **Homogeneity property means a system which produces an output

*y*(

*n*) for an input

*x*(

*n*) must produce an output

*ay*(

*n*) for an input

*ax*(

*n*).

**Q.39. ***What is superposition property?*

** Ans. **Superposition property means a system which produces an output

*y*

_{1}(

*n*) for an

input *x*_{1}(*n*) and an output *y*_{2}(*n*) for an input *x*_{2}(*n*) must produce an output *y*_{1}(*n*) + *y*_{2}(*n*) for an input *x*_{1}(*n*) + *x*_{2}(*n*).

**Q.40. ***Define a linear system.*

** Ans. **A linear system is a system which obeys the principle of superposition and the principle of homogeneity.

**Q.41. ***Define a non-linear system.*

** Ans. **A non-linear system is a system which does not obey the principle of superposition and principle of homogeneity.

**Q.42. ***Define a shift-invariant system.*

** Ans. **A shift-invariant system is a system whose input/output characteristics do not change with time, i.e. a system for which a time shift in the input results in a corresponding time shift in the output.

**Q.43. ***Define a shift-variant system.*

** Ans. **A shift-variant system is a system whose input/output characteristics change with time, i.e. a system for which a time shift in the input does not result in a corresponding time shift in the output.

**Q.44. ***Define a bounded input-bounded output stable system.*

** Ans. **A bounded input-bounded output stable system is a system which produces a bounded output for every bounded input.

**Q.45. ***Define an unstable system.*

** Ans. **An unstable system is a system which produces an unbounded output for a bounded input.

**Q.46. ***What is an invertible system?*

** Ans. **An invertible system is a system which has a unique relationship between its input and output.

**Q.47. ***What is a non-invertible system?*

** Ans. **A non-invertible system is a system which does not have a unique relationship between its input and output.

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