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Choose the function 
for which a Fourier series cannot be defined
Select one:
for which a Fourier series cannot be definedSelect one:
- a)1
- b)4cos(20t + 3) + 2sin(710t)
- c)exp(–|t|) sin(25t)
- d)3sin(25t)
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
Choose the functionfor which a Fourier series cannot be definedSelect ...
→ 3sin(25t) is periodic ω = 25.
→ 4cos(20t + 3) + 2sin(710t) sum of two periodic function is also periodic function
→ e
sin 25t Due to decaying exponential decaying function it is not periodic.
So Fourier series cannot be defined for it.
→ Constant, Fourier series exists.
Fourier series can’t be defined for option (c).
The correct answer is: exp(–|t|) sin(25t)
→ 4cos(20t + 3) + 2sin(710t) sum of two periodic function is also periodic function
→ e
sin 25t Due to decaying exponential decaying function it is not periodic.So Fourier series cannot be defined for it.
→ Constant, Fourier series exists.
Fourier series can’t be defined for option (c).
The correct answer is: exp(–|t|) sin(25t)
Most Upvoted Answer
Choose the functionfor which a Fourier series cannot be definedSelect ...
For Fourier series the function should be single valued but in option c the function is not single valued in the negative half of the range the function has an exponentially increasing part but in the positive section of the given region the function has an exponentially decaying term so in different regions of the range of the given function it has different values so it is not a single valued function so Fourier series cannot be defined for this function
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