Continuous Time Signal Analysis

Digital Communications Systems

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

1. The Fourier series representation of any signal x(t) is defined as ___________
a) ∑∞k=−∞ckej2πkF0t
b) ∑∞k=0ckej2πkF0t
c) ∑∞k=−∞cke−j2πkF0t
d) ∑∞k=−∞c−kej2πkF0t
t.

2. Which of the following is the equation for the Fourier series coefficient?
a) 1Tp∫t0+Tp0x(t)e−j2πkF0tdt
b) 1Tp∫∞t0x(t)e−j2πkF0tdt
c) 1Tp∫t0+Tpt0x(t)e−j2πkF0tdt
d) 1Tp∫t0+Tpt0x(t)ej2πkF0tdt

3. Which of the following is a Dirichlet condition with respect to the signal x(t)?
a) x(t) has a finite number of discontinuities in any period
b) x(t) has finite number of maxima and minima during any period
c) x(t) is absolutely integrable in any period
d) all of the mentioned

4. The equation x(t)=∑∞k=−∞ckej2πkF0t is known as analysis equation.
a) True
b) False

5. Which of the following is the Fourier series representation of the signal x(t)?
a) c0+2∑∞k=1|ck|sin(2πkF0t+θk)
b) c0+2∑∞k=1|ck|cos(2πkF0t+θk)
c) c0+2∑∞k=1|ck|tan(2πkF0t+θk)
d) None of the mentioned

6. The equation x(t)=a0+∑∞k=1(akcos2πkF0t–bksin2πkF0t) is the representation of Fourier series.
a) True
b) False

7. The equation of average power of a periodic signal x(t) is given as ___________
a) ∑∞k=0|ck|2
b) ∑∞k=−∞|ck|
c) ∑0k=−∞|ck|2
d) ∑∞k=−∞|ck|2

8. What is the spectrum that is obtained when we plot |ck |2 as a function of frequencies kF0, k=0,±1,±2..?
a) Average power spectrum
b) Energy spectrum
c) Power density spectrum
d) None of the mentioned

9. What is the spectrum that is obtained when we plot |ck| as a function of frequency?
a) Magnitude voltage spectrum
b) Phase spectrum
c) Power spectrum
d) None of the mentioned

10. What is the equation of the Fourier series coefficient ck of an non-periodic signal?
a) 1Tp∫t0+Tp0x(t)e−j2πkF0tdt
b) 1Tp∫∞−∞x(t)e−j2πkF0tdt
c) 1Tp∫t0+Tpt0x(t)e−j2πkF0tdt
d) 1Tp∫t0+Tpt0x(t)ej2πkF0tdt

11. Which of the following relation is correct between Fourier transform X(F) and Fourier series coefficient ck?
a) ck=X(F0/k)
b) ck= 1/TP (X(F0/k))
c) ck= 1/TP(X(kF0))
d) none of the mentioned

12. According to Parseval’s Theorem for non-periodic signal, ∫∞−∞|x(t)|2dt.
a) ∫∞−∞|X(F)|2dt
b) ∫∞−∞|X∗(F)|2dt
c) ∫∞−∞X(F).X∗(F)dt
d) All of the mentioned

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