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F(t) is a periodic square wave function as shown. It takes only two values, 4 and 0, and stays at each of these values for 1 second before changing. What is the constant term in the Fourier series expansion of F(t)?
  • a)
    1
  • b)
    2
  • c)
    3
  • d)
    4
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
F(t) is a periodic square wave function as shown. It takes only two va...
Fourier Series is defined as

Calculation:
Given:
f(t) is an even periodic function, Since
f(-t) = f(t)
The constant term in the Fourier series is: ao/2

Since the function is not continious, we need to break the integral according to interval
from -1 to 0, f(t) = 0,
from 0 to 1, f(t) = 4

The constant term is:

Mistake Points
Avoid using the integral property of even function because the given function f(t) is not continuous. Though the function given is an even periodic function but it is not continuous.
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