## Digital Signal Processing Questions and Answers Part-3

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

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;u(n)=0 for n<0 is an _____________
a) Unit sample signal
b) Unit step signal
c) Unit ramp signal
d) None of the mentioned

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 a unit ramp signal.

3. The phase function of a discrete time signal x(n)=an, where a=r.e is?
a) tan(nθ)
b) nθ
c) tan-1(nθ)
d) none of the mentioned

Explanation: Given x(n)=an=(r.e)n = rn.ejnθ
=>x(n)=rn.(cosnθ+jsinnθ)
Phase function is tan-1(cosnθ/sinnθ)=tan-1(tan nθ)=nθ.

4. The signal given by the equation $$\sum_{n=-{\infty}}^{\infty}|x(n)|^2$$ is known as __________
a) Energy signal
b) Power signal
c) Work done signal
d) None of the mentioned

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)

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

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))

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

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)=Brn where r=eαT to be called as an decaying exponential signal?
a) 0<r<∞
b) 0<r<1
c) r>1
d) r<0