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I have this question of whether it is possible to represent non-periodic functions in a form just like you would represent a periodic function through a Fourier series.

I understand this question may seem vague but I hope you understand my question. Further EDITS subject to need for clarity.

PS - I understand from a previous post (Can any continous,bounded function have a fourier series?) that you can't represent continuous bounded functions as Fourier series.

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Of course not, as the sum of a convergent Fourier series is itself periodic. However, you can typically generate a Fourier representation that is good over some bounded interval. –  Mark McClure May 31 '13 at 0:11
    
Yes, I understand. But I want a series like the Fourier Series that can best represent continuous functions... –  Jugesh Sundram May 31 '13 at 0:14
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Ahh... "Fourier like" - perhaps, you could be more specific? The key thing about the sines and cosines as used in Fourier series is their orthogonality. There are many families of orthogonal functions that can be used in a similar manner. Whether one of these families can help depends greatly on your application what properties you desire the result to have. That's the sense in which you'll really need to be more precise, if you want a solid answer. –  Mark McClure May 31 '13 at 0:37
    
Sounds like you may be interested in quasiperiodic functions. –  ˈjuː.zɚ79365 May 31 '13 at 5:46
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