100% satisfaction guarantee Immediately available after payment Both online and in PDF No strings attached
logo-home
Previously searched by you
Previously searched by you
logo
Fourier Series Exam Questions With Correct Answers. $10.49   Add to cart
Quickly navigate to
Preview
  2.  
  3. Fourier Series
  4.  
  5. Fourier Series

Exam (elaborations)

Fourier Series Exam Questions With Correct Answers.
 1 view  0 purchase
  • Course
  • Fourier Series
  • Institution
  • Fourier Series

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...

[Show more]

Preview 1 out of 4  pages

Document information

  • August 17, 2024
  • 4
  • 2024/2025
  • Exam (elaborations)
  • Questions & answers

Subjects

  • fourier series exam questions with correct answers

Written for

  • Fourier Series
  • Fourier Series

Seller

avatar-seller
Brightstars

Content preview

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:

The benefits of buying summaries with Stuvia:

Guaranteed quality through customer reviews

Guaranteed quality through customer reviews

Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.

Quick and easy check-out

Quick and easy check-out

You can quickly pay through credit card or Stuvia-credit for the summaries. There is no membership needed.

Focus on what matters

Focus on what matters

Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!

Frequently asked questions

What do I get when I buy this document?

You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.

Satisfaction guarantee: how does it work?

Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.

Who am I buying these notes from?

Stuvia is a marketplace, so you are not buying this document from us, but from seller Brightstars. Stuvia facilitates payment to the seller.

Will I be stuck with a subscription?

No, you only buy these notes for $10.49. You're not tied to anything after your purchase.

Can Stuvia be trusted?

4.6 stars on Google & Trustpilot (+1000 reviews)

73314 documents were sold in the last 30 days

Founded in 2010, the go-to place to buy study notes for 14 years now

Start selling
$10.49
  • (0)
  Add to cart