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Which of the following statements regarding the Fourier series are correct?

A. For an even symmetry, only sine terms exist.

B. For an even symmetry, only cosine terms exist.

C. For an odd symmetry, only cosine terms exist.

D. For an odd symmetry, only sine terms exist.

Choose the correct answer from the options given below:

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UGC NET Paper 2: Electronic Science 3rd Dec 2021 Shift 2
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  1. A and C only 
  2. B and D only
  3. C and D only
  4. A and D only 

Answer (Detailed Solution Below)

Option 2 : B and D only
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Detailed Solution

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Consider the following table for Relationship between time domain signal and trigonometric F.S coefficient

Time domain

Trigonometric F.S. coefficient

 1. real and even

 bn = 0  an ≠ 0

 2. Real and odd

 bn ≠ 0  an = 0

 3. real + half wave summitry

 an = bn = 0 (n = even) a0 = 0

 4. Real + Even + HWS

 bn = 0   a0 = 0    an = 0 if n = even

 5. Real + ODD + HWS

 a0 = 0

 an = 0

 bn = 0 → n = even

 

 

For an even symmetry, only cosine terms exist.
For an odd symmetry, only sine terms exist.

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Q1.Which of the following statements regarding the Fourier series are correct? A. For an even symmetry, only sine terms exist. B. For an even symmetry, only cosine terms exist. C. For an odd symmetry, only cosine terms exist. D. For an odd symmetry, only sine terms exist. Choose the correct answer from the options given below:
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