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.ejθ is?
a) tan(nθ)
b) nθ
c) tan-1(nθ)
d) none of the mentioned
Explanation: Given x(n)=an=(r.ejθ)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
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; x(n)=0, for n≠0 is a _____________
a) Step function
b) Ramp function
c) Triangular function
d) Impulse function
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.