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 June 19th, 2010, 02:03 AM #1 Newbie   Joined: Jun 2010 Posts: 2 Thanks: 0 Discrete fourier vs fourier transform Hi, I have some questions regarding basic understanding of Fourier transformation 1)Using discrete fourier transform, you only analyse for some frequencies. Do you analyse for a range of frequencies, frequencies with a given interval or only specific frequencies? 2) What are the advatages of discrete fourier compared with "normal" fourier? 3) What is windowed fourier? and when is that used? 4) What are the advantages of Fourier and wavelet respectively? It would help a lot, if anyone could answer these questions, without too much math Thanks, Beckie
 June 19th, 2010, 01:04 PM #2 Global Moderator   Joined: May 2007 Posts: 6,822 Thanks: 723 Re: Discrete fourier vs fourier transform Fourier analysis is divided into two broad categories. Fourier series, where the function is defined over a finite interval, and is implicitly (or explicitly) periodic outside the interval. Fourier transforms are defined for functions defined over an infinite interval and belong to to some Lp class for p ? 1.
 June 20th, 2010, 12:16 AM #3 Newbie   Joined: Jun 2010 Posts: 2 Thanks: 0 Re: Discrete fourier vs fourier transform When you say a finit interval, do you mean time interval or frequency interval? what does Lp class mean?!? Do you know any answers to my specific questions? Cause I really need to know it by monday
June 20th, 2010, 12:58 PM   #4
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Re: Discrete fourier vs fourier transform

Quote:
 Originally Posted by beckie When you say a finit interval, do you mean time interval or frequency interval? what does Lp class mean?!? Do you know any answers to my specific questions? Cause I really need to know it by monday
Your questions tell me that you are involved in an engineering course. My background is mathematics, so I can't answer your questions directly.

When I said finite interval, I meant that the function f(x) is defined over a finite interval and can be represented by a Fourier series consisting of a constant plus cosines and sines of qnx, where q is a constant determined by the interval while n ranges over all positive integers. For example if the interval is of length 1, q=2?.

A function f(x) belongs to an Lp class if the integral over the real line of |f(x)|^p exists. Most Fourier analysis studies are concerned with p = 1 or 2.

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