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Fourier Series: Noise Cancelling Headphones

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Hi guys,

I was wondering if investigating the Fourier Series, and its applications for Noise Cancelling Headphones would be a good and suitable Math HL IA?

I'm not sure if it has the appropriate level of complexity, and also if 'investigating' i.e. explaining how this system works in noise cancelling headphones is going to score highly. Should I try and narrow it down, focussing on a particular brand? Also, how can I make it more 'mathematical' as exploring one theorem may not should a great use of maths?

Has anyone done any work on the Fourier Theorem or series already and found that there isn't much to explore?

If anyone has any comments, tips or advice on this particular field or on the IA in general, I would be very appreciative.

Thanks a lot :)

John

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When it comes to an IA, a lot of research is required. I think honestly this would be a great topic, but you need to think about the main question on hand.

Here is a site I found that might be useful.

http://www.wired.com/2011/05/st_equation_noisecanceled/

& also you could use fibonacci numbers and the conventional discrete fourier transform

Edited by Lew Talon

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I tried doing my Math IA on Fourier series and their application in music (frequencies, etc). However, you will not find any material whatsoever out there on the Internet. I even had to mail professors and they shared that opinion. I spent approximately 10 hours looking for anything more than simple calculations and explanations but to no vain.

I suggest you change topic.

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I actually think you should go for it. I enjoyed my IA which was on the Fourier Series. I initially started on the Fourier Transformation, but that proved much more difficult so I stuck with the series. In terms of the noise cancelling headphones though, that could be difficult. I recommend you do a little bit of research on it to see if you like it because you'll be doing a lot of reading on it. My IA was on the Fourier Series and how it applies to electronic music, specifically subtractive and some fm synthesis. I thought it was interesting because it heavily applied to my interests, but if the Fourier Series doesn't apply to your interests at all, then I'd stay away from it. Either way, good luck!

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Thanks a lot guys. I was wondering whether or not I should have sample 'calculations' i.e. using the formula that I found and modified and just chuck in numbers to show how the Fourier Transform comes up with the destructive wave?

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Fourier series and Fourier transforms are a great topic, as they have such a wide breadth of applications. I'd suggest having a look at the MIT OpenCourseware website, specifically Gilbert Strang's courses, and Arthur Mattuck's. You could investigate how they are used to solve differential equations analytically (see the heat equation).

 

Alternatively, you could investigate how they are applied in numerical methods to solve differential equations (see the fast Fourier transform and fast Poisson solver.)

 

If you'd like to stick to just Fourier series, you could derive the standard series in terms of cosine and sine, and then derive the general Fourier series which can be used for any set of functions which satisfy the orthogonality relation. 

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I actually think you should go for it. I enjoyed my IA which was on the Fourier Series. I initially started on the Fourier Transformation, but that proved much more difficult so I stuck with the series. In terms of the noise cancelling headphones though, that could be difficult. I recommend you do a little bit of research on it to see if you like it because you'll be doing a lot of reading on it. My IA was on the Fourier Series and how it applies to electronic music, specifically subtractive and some fm synthesis. I thought it was interesting because it heavily applied to my interests, but if the Fourier Series doesn't apply to your interests at all, then I'd stay away from it. Either way, good luck!

Hi I'm thinking of doing my IA on a similar topic, but I'm completely lost on what to really say I'm "exploring " with the fourier series and music. Could you possibly give me sone tips on how to phrase it and what I should zone in on with the specifics. I'm really lost and desperately nead help!!!

Thanks.

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I am also interested in using the Fourier series as the topic for my Math IA. I however, don't know how to use actual mathematics in it. I can describe my interest, and describe how it might be used. But how can I display my mathematical knowledge using this topic? 

 

Thanks. 

Edited by Aditya123

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On 5/13/2014 at 8:25 AM, DRiPX said:

I actually think you should go for it. I enjoyed my IA which was on the Fourier Series. I initially started on the Fourier Transformation, but that proved much more difficult so I stuck with the series. In terms of the noise cancelling headphones though, that could be difficult. I recommend you do a little bit of research on it to see if you like it because you'll be doing a lot of reading on it. My IA was on the Fourier Series and how it applies to electronic music, specifically subtractive and some fm synthesis. I thought it was interesting because it heavily applied to my interests, but if the Fourier Series doesn't apply to your interests at all, then I'd stay away from it. Either way, good luck!

Hey, even I was planning to do my Math HL IA on Fourier Series, however, I am completely lost. It would be great if you could guide me how to go about and if possible can you share your IA, so I can get an idea about it. 

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@Aditya123 Then you should probably learn the basics of Fourier Series. It is too risky to discuss maths you do not comprehend. 

@Rocky_2704 You have to understand that sometimes a student in 2014 may not be reachable in 2019. In general when doing IA of topic outside of the syllabus, you should first thoroughly explain how it works and what it does. Then you can do some examples or use FS to solve a long problem. You can also include some applications of FS. Finally, you should at times make connections between FS and core HL Math, so you are getting a good score in "Use of Mathematics". As for "Personal Engagement", do not simply state "I love FS", instead walk through your struggles of how you came to understand FS and note down any curious points you have while learning FS. 

Edited by kw0573

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