# Discrete-Time Signals and Systems Viva Questions

## 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

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:

1. Graphical representation
2. Functional representation
3. Tabular representation
4. Sequence representation

Q.5. Define unit step sequence.

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

u(n)=\left\{\begin{matrix}1 & for & n\geq 0 \\0 & for & n< 0 \\\end{matrix}\right.

Q.6. Define unit ramp sequence.

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

r(n)=\left\{\begin{matrix}1 & for & n\geq 0 \\0 & for & n < 0 \\\end{matrix}\right.

Or r(n)= nu(n)

Q.7. Define unit parabolic sequence.

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

p(n)=\left\{\begin{matrix}\frac{n^{2}}{2} & for & n\geq 0 \\0 & for & n < 0 \\\end{matrix}\right.

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:

\delta(n)=\left\{\begin{matrix}1 & for & n= 0 \\0 & for & n \neq 0 \\\end{matrix}\right.

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

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

1. \delta (n)=u(n)-u(n-1)
2. \delta(n-k)=\left\{\begin{matrix}1, & n=k \\0, & n\neq k \\\end{matrix}\right.
3. 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 (ω0n +ϕ)

where ω0 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) = anu(n)

where a is a constant.

Q.12. Define complex exponential signal.

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

x(n)=a^{n}e^{j(\omega _{0}n+\phi )}

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:

1. Time shifting
2. Time reversal
3. Time scaling
4. Amplitude scaling
6. 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:

1. Deterministic and random signals
2. Periodic and aperiodic signals
3. Energy and power signals
4. Even and odd signals
5. 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 ω0 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(m0) 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:

E=\displaystyle \lim_{N \to \infty }\sum_{n=-N}^{N}\begin{vmatrix} x(n)\end{vmatrix}^{2}

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

x_{e}(n)=\frac{1}{2}[x(n)+x(-n)] x_{0}(n)=\frac{1}{2}[x(n)-x(-n)]

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:

1. Static (memoryless) and dynamic (memory) systems
2. Causal and non-causal systems
3. Linear and non-linear systems
4. Time-invariant and time-varying systems
5. Stable and unstable systems.
6. 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 y1(n) for an

input x1(n) and an output y2(n) for an input x2(n) must produce an output y1(n) + y2(n) for an input x1(n) + x2(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.