31. Is the system with impulse response h(n)=2nu(n-1) stable.
A. True
B. False
Answer: B
Let S=\(\sum_{n=-{\infty}}^{\infty}|h(n)|\)
=\(\sum_{n=-{\infty}}^{\infty}2^n u(n-1)\)
=\(\sum_{n=-{\infty}}^{\infty}2^n\)
=2+4+8+…=∞
So, the system is not stable.
31. If x(n) is a discrete-time signal, then the value of x(n) at the non-integer value of ‘n’ is?
A. Zero
B. Positive
C. Negative
D. Not defined
Answer: D
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.
32. 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
Answer: C
When we plot the graph for the given function, we get a straight line passing through the origin with a unit positive slope. So, the function is called a unit ramp signal.
33. The phase function of a discrete-time signal x(n)=an, where a=r.ejθ is?
A. tan(nθ)
B. nθ
C. tan-1(nθ)
D. none of the mentioned
Answer: B
Given x(n)=an=(r.ejθ)n = rn.ejnθ
=>x(n)=rn.(cosnθ+jsinnθ)
Phase function of a discrete-time signal x(n)=an is
tan-1(cosnθ/sinnθ)=tan-1(tan nθ)=nθ.
34. The signal given by the equation $\mathop \sum \limits_{n = – \infty }^\infty |x(n){|^2}$ is known as __________
A. Energy signal
B. Power signal
C. Work done signal
D. None of the mentioned
Answer: A
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 the Energy signal.
35.The given signal x(n) × δ(n-k)=?
A. x(n)
B. x(k)
C. x(k) × δ(n-k)
D. x(k) × δ(k)
Answer: C
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).
36. 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
Answer: B
According to the definition of an 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).
37. 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))
Answer: D
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)).
38. Time scaling operation is also known as ___________
A. Down-sampling
B. Up-sampling
C. Sampling
D. None of the mentioned
Answer: A
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 down-sampling.
39. What is the condition for a signal x(n)=Brn where r=eαT to be called a decaying exponential signal?
A. 0<r<∞
B. 0<r<1
C. r>1
D. r<0
Answer: B
When the value of ‘r’ lies between 0 and 1 then the value of x(n) goes on decreasing exponentially with an increase in the value of ‘n’. So, the signal is called a decaying exponential signal.</r<1 </r<∞
40. The function given by the equation x(n)=1, for n=0; x(n)=0, for n≠0 is a _______
A. Step function
B. Ramp function
C. Triangular function
D. Impulse function
Answer: D
The function given by the equation x(n)=1, for n=0; x(n)=0, for n≠0 is a Impulse function.
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.
