This set of Digital Signal Processing Multiple Choice Questions & Answers (MCQs) focuses on ” Discrete Time Signals”.

1. If x(n) is a discrete-time signal, then the value of x(n) at non integer value of ‘n’ is:

a) Zero

b) Positive

c) Negative

d) Not defined

View Answer

Explanation: For a discrete time signal, the value of x(n) exists only at integral values of n. So, for a non- integer value of ‘n’ the value of x(n) does not exist.

2. The discrete time function defined as u(n)=n for n≥0;=0 for n<0 is an:

a) Unit sample signal

b) Unit step signal

c) Unit ramp signal

d) None of the mentioned

View Answer

Explanation: When we plot the graph for the given function, we get a straight line passing through origin with a unit positive slope. So, the function is called as unit ramp signal.

3.The phase function of a discrete time signal x(n)=a^{n}, where a=r.e^{jθ} is:

a) tan(nθ)

b) nθ

c) tan^{-1}(nθ)

d) None of the mentioned

View Answer

Explanation: Given x(n)=a

^{n}=(r.e

^{jθ})

^{n}=r

^{n}.e

^{jnθ}

=>x(n)=r

^{n}.(cosnθ+jsinnθ)

Phase function is tan

^{-1}(cosnθ/sinnθ)=tan

^{-1}(tan nθ)=nθ.

4. The signal given by the equation is known as:

a) Energy signal

b) Power signal

c) Work done signal

d) None of the mentioned

View Answer

Explanation: We have used the magnitude-squared values of x(n), so that our definition applies to complex-valued as well as real-valued signals. If the energy of the signal is finite i.e., 0<E<∞ then the given signal is known as Energy signal.

5. x(n)*δ(n-k)=?

a) x(n)

b) x(k)

c) x(k)*δ(n-k)

d) x(k)*δ(k)

View Answer

Explanation: The given signal is defined only when n=k by the definition of delta function. So, x(n)*δ(n-k)= x(k)*δ(n-k).

6. A real valued signal x(n) is called as anti-symmetric if:

a) x(n)=x(-n)

b) x(n)=-x(-n)

c) x(n)=-x(n)

d) None of the mentioned

View Answer

Explanation: According to the definition of anti-symmetric signal, the signal x(n) should be symmetric over origin. So, for the signal x(n) to be symmetric, it should satisfy the condition x(n)=-x(-n).

7. The odd part of a signal x(t) is:

a) x(t)+x(-t)

b) x(t)-x(-t)

c) (1/2)*(x(t)+x(-t))

d) (1/2)*(x(t)-x(-t))

View Answer

Explanation: Let x(t)=xe(t)+xo(t)

=>x(-t)=xe(-t)-xo(-t)

By subtracting the above two equations, we get

xo(t)=(1/2)*(x(t)-x(-t)).

8. Time scaling operation is also known as:

a) Down-sampling

b) Up-sampling

c) Sampling

d) None of the mentioned

View Answer

Explanation: If the signal x(n) was originally obtained by sampling a signal xa(t), then x(n)=xa(nT). Now, y(n)=x(2n)(say)=xa(2nT). Hence the time scaling operation is equivalent to changing the sampling rate from 1/T to 1/2T, that is to decrease the rate by a factor of 2. So, time scaling is also called as down-sampling.

9. What is the condition for a signal x(n)=Br^{n} where r=e^{αT} to be called as an decaying exponential signal?

a) 0<r<∞

b) 0<r<1

c) r>1

d) r<0

View Answer

Explanation: When the value of ‘r’ lies between 0 and 1 then the value of x(n) goes on decreasing exponentially with increase in value of ‘n’. So, the signal is called as decaying exponential signal.

10. The function given by the equation x(n)=1, for n=0;=0, for n≠0 is a:

a) Step function

b) Ramp function

c) Triangular function

d) Impulse function

View Answer

Explanation: According to the definition of the impulse function, it is defined only at n=0 and is not defined elsewhere which is as per the signal given.

**Sanfoundry Global Education & Learning Series – Digital Signal Processing.**

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