# Symmetry Properties of the Fourier Series MCQ’s

This set of Signals & Systems Multiple Choice Questions & Answers (MCQs) focuses on “Symmetry Properties of the Fourier Series”.

1. What is the function of an even signal?
a) x(t) = -x(t)
b) x(t) = x(-t)
c) x(t) = -x(-t)
d) x(t) = x(t+1)

2. What is the function of an odd signal?
a) x(t) = -x(t)
b) x(t) = x(-t)
c) x(t) = -x(-t)
d) x(t) = x(t+1)

3. How can fourier series calculations be made easy?
a) Using symmetry conditions
b) Using formula
c) Using integration
d) Calculations are easy anyways

4. What is the product of an even signal and odd signal?
a) Even signal
b) Odd signal
c) Mixture of even and odd
d) Odd signals sometimes

5. What are the values of an and bn when the signal is even?
a) an=0 and bn=0
b) an=0 and bn=4/T∫x(t)sin(nwt)dt
c) an=4/T∫x(t)cos(nwt)dt and bn=0
d) an=4/T∫x(t)sin(nwt)dt and bn=4/T∫x(t)cos(nwt)dt

6. How can we define the coefficients half wave symmetry when n is even?
a) an=0 and bn=0 and a0=0
b) an=4/T∫x(t)cos(nwt)dt and bn=0= a0
c) an=4/T∫x(t)sin(nwt)dt and bn=4/T∫x(t)cos(nwt)dt and a0=0
d) an=4/T∫x(t)sin(nwt)dt and bn=4/T and a0=0

7. What are the values of an and bn when the signal is even?
a) an=0 and bn=0
b) an=0 and bn=4/T∫x(t)cos(nwt)dt
c) an=4/T∫x(t)cos(nwt)dt and bn=0
d) an=4/T∫x(t)sin(nwt)dt and bn=4/T∫x(t)cos(nwt)dt

8. How can we define half wave symmetry?
a) x(t) = -x(t±T)
b) x(t) = x(t±T/2)
c) x(t) = x(t±T)
d) x(t) = -x(t±T/2)

9. How can we define the coefficients a half wave symmetry when n is even?
a) an=0 and bn=0 and a0=0
b) an=4/T∫x(t)cos(nwt)dt and bn=0= a0
c) an=4/T∫x(t)sin(nwt)dt and bn=4/T∫x(t)cos(nwt)dt and a0=0
d) an=4/T∫x(t)sin(nwt)dt and bn=4/T and a0=0

10. What are the types of symmetry shown by signals?
a) Even symmetry and odd symmetry
b) Even, odd and quarter wave symmetry
c) Even, odd, half-wave and quarter wave symmetry
d) Half wave symmetry

11. When does a wave posses a quarter wave symmetry?
a) It has either even or odd symmetry
b) It has half wave symmetry
c) even/odd symmetry and half wave symmetry
d) It is even in one quarter and odd in the other