Fourier series, applications to sound

In summary, the conversation is about understanding a mathematical problem involving integrations and the confusion over the denominator in the solution. One person suggests doing the integration oneself to better understand it, while the other person presents their own derivation which leads to confusion. Eventually, the issue is resolved.
  • #1
robertjford80
388
0

Homework Statement



Screenshot2012-06-18at13057AM.png



The Attempt at a Solution



I don't understand where that 2 comes from in the denominator in cos nπ/2
 
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  • #2
robertjford80 said:

Homework Statement



Screenshot2012-06-18at13057AM.png



The Attempt at a Solution



I don't understand where that 2 comes from in the denominator in cos nπ/2

Instead of trying to follow somebody else's presentation, just sit down and do the integrations yourself. That way, you will answer your own question, and will *understand it much better than if somebody else showed you how to do it*. I really believe that.

RGV
 
  • #3
of course i always do my own derivation. my own derivation is -cosnπ/524nπ - 1/524nπ

There, I'm still as clueless I was before.
 
  • #4
robertjford80 said:
of course i always do my own derivation. my own derivation is -cosnπ/524nπ - 1/524nπ

There, I'm still as clueless I was before.

So, you claim that 524/1048 = 1? That is the only way you could end up with what you said.

RGV
 
  • #5
ok, I got it.
 

Related to Fourier series, applications to sound

1. What is a Fourier series?

A Fourier series is a mathematical representation of a periodic function in terms of a sum of sine and cosine waves. It allows for the decomposition of a complex signal into simpler components, making it easier to analyze and understand.

2. How is a Fourier series used in sound?

A Fourier series is commonly used in sound engineering to analyze and manipulate sound waves. By breaking down a sound wave into its individual frequency components, we can understand how different frequencies contribute to the overall sound and make adjustments as needed.

3. What are some common applications of Fourier series in sound?

Some common applications of Fourier series in sound include noise reduction, equalization, and synthesis. By understanding the frequency components of a sound, we can apply filters and effects to manipulate the sound in various ways.

4. What are the limitations of Fourier series in sound analysis?

One limitation of Fourier series is that it assumes the signal is periodic, which is not always the case in sound. This can lead to inaccuracies in the analysis of non-periodic sounds. Additionally, Fourier series does not take into account factors such as timbre and envelope, which are important in describing the quality and character of a sound.

5. How has the use of Fourier series in sound evolved over time?

The use of Fourier series in sound has evolved significantly with advancements in technology. In the past, it was primarily used for basic analysis and manipulation of sound waves. Now, it is used in more complex algorithms for tasks such as speech recognition and audio compression. It has also been combined with other mathematical techniques, such as wavelets, to improve its accuracy and functionality.

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