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Fourier Series Exam Questions With Correct Answers.
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Fourier Series Exam Questions With Correct Answers. A function is periodic if.. - answerf(x+P) = f(x) What is the least period of a function? - answerThe smallest value for P for which f(x+P) = f(x) What is a Fourier series? - answerA way of writing almost any periodic function as a sum of tr...

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  • August 17, 2024
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  • 2024/2025
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  • fourier series exam questions with correct answers

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BRIGHTSTARS EXAM STUDY SOLUTIONS 8/15/2024 2:05 PM



Fourier Series Exam Questions With Correct
Answers.

A function is periodic if.. - answer✔✔f(x+P) = f(x)

What is the least period of a function? - answer✔✔The smallest value for P for which f(x+P) =
f(x)

What is a Fourier series? - answer✔✔A way of writing almost any periodic function as a sum of
trigonometric functions/sinusoidal oscillations with frequencies integer multiples of the
fundamental 1/P (harmonics)
Done by identifying a complete set (basis of functions) to identify all elements in an infinite
dimensional function space

When will a Fourier series converge? - answer✔✔If the derivative of the series is square
integrable (i.e ∫ |f'(x)|²dx exists - integral over whole domain, x₀ to x₀ + P)

Equation for a Fourier series? - answer✔✔F(x) = a₀/2 + ∑ (aₙ cos(nπx/L) + bₙsin(nπx/L))

Definition of orthogonality of functions? - answer✔✔Functions defined on the same domain are
orthogonal iff:
∫ f(x)g(x)dx = 0

What is an orthonormal basis? - answer✔✔A basis in which the basis vectors/functions are unit
vectors that are all orthogonal to each other

Basis vectors of Rⁿ - answer✔✔(1,0,0...0) to (0,0,....1)
Integral is between -L and L:

∫ cosmx cosnx dx = - answer✔✔2L if m = n = 0
L if m = n ≠ 0
0 if m ≠ n
Integral is between -L and L:

∫ cosmx sinnx dx = - answer✔✔0 for all m and n
Integral is between -L and L:

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