Can the Orthonormality Property Help Calculate Fourier Series Coefficients?

  • Thread starter Thread starter kolycholy
  • Start date Start date
  • Tags Tags
    Property
Click For Summary

Discussion Overview

The discussion revolves around the calculation of Fourier series coefficients using the orthonormality property. Participants explore the relationship between the scalar product of a function and its Fourier series representation, questioning the underlying principles and derivations involved.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Homework-related

Main Points Raised

  • One participant presents the equation for a function x(t) expressed as a Fourier series and questions how the orthonormality property can be used to calculate the coefficients z[m].
  • Another participant prompts the original poster to compute the scalar product to clarify their understanding.
  • A subsequent reply indicates that the book has already computed the scalar product, but the participant remains confused about the equality of z[m] and the scalar product.
  • Another participant suggests that the confusion may stem from a lack of understanding of the derivation process and asks for specifics on what is unclear.
  • One participant offers a link to additional resources that may assist in learning how to calculate the Fourier series coefficients.

Areas of Agreement / Disagreement

The discussion reflects a lack of consensus, with participants expressing confusion and seeking clarification on the derivation of the relationship between the scalar product and the Fourier coefficients. Multiple viewpoints on the understanding of the concept are present.

Contextual Notes

Participants have not fully resolved the assumptions or steps involved in the derivation of the Fourier series coefficients using the orthonormality property, leading to ongoing questions and uncertainties.

Who May Find This Useful

This discussion may be useful for students learning about Fourier series, particularly those grappling with the concepts of orthonormality and scalar products in the context of signal processing or mathematical analysis.

kolycholy
Messages
38
Reaction score
0
x(t) = sigma (from m = -infinity to infinity) zm e^(j*m*omega*t)

now my book says that using orthonormality property, we can calculate zm by calculating scalar product of x(t) and em(t) (where em(t) = e^(j*m*omega*t))
hows that possible??

please feel free to move the thread if its in wrong section!
 
Last edited:
Engineering news on Phys.org
Have you tried actually computing the scalar product?
 
Hurkyl said:
Have you tried actually computing the scalar product?
the book has done that for me ...
it still makes no sense why zm would equal the scalar product
 
Since you probably didn't come here just to say you're surprised, that means you don't understand something about the derivation -- so what didn't you understand?
 

Similar threads

  • · Replies 1 ·
Replies
1
Views
2K
  • · Replies 4 ·
Replies
4
Views
3K
  • · Replies 17 ·
Replies
17
Views
2K
  • · Replies 1 ·
Replies
1
Views
3K
Replies
3
Views
2K
  • · Replies 3 ·
Replies
3
Views
1K
  • · Replies 4 ·
Replies
4
Views
4K
Replies
4
Views
2K
Replies
19
Views
3K
  • · Replies 0 ·
Replies
0
Views
2K