# What is fourier series/fourier transform?

1. Sep 21, 2011

### quietrain

can anyone give me a simple explanation what fourier analysis is all about? i have read wiki and it is a little confusing

what am i doing when i express a funciton as a series? what is the difference to a transform?

i know how to follow the steps of a fourier series/transform, but i have no idea why i am doing it?

thanks!

2. Sep 21, 2011

### quietrain

assuming i have a function f(x) = x

what does it mean to take the fourier series?

what does it mean to take hte fourier transform?

3. Sep 21, 2011

### mathman

4. Sep 22, 2011

### quietrain

is fourier series something like taylor expansion? where greater powers of the terms give better accuracy of the particular function?

5. Sep 22, 2011

### quietrain

i refer you to the section "introduction" , where at the end of this section, they described the fourier transform as decomposing an oscillating function into several sines and cosines.

if i understood correctly what the 4 graphs are saying, does it mean that when i fourier transform the first graph (blue), i will get a transformed that is (green, when i sub 3 hz into the fourier transformed expression) and (red when i sub in 5hz into the fourier transformed expression)

and when i integrate these 2 expressions, i will get 0.5(green) and 0.000.... (red)

so the value 0.5 and 0.0000... is akin to telling me the fraction of blue graph that oscillates at 3 hz is 0.5, while the fraction of blue graph that oscillates at 5hz is 0.0000...?

is this what fourier transform is about?

thanks!

6. Sep 22, 2011

### paulfr

A Fourier Series approximation of a periodic waveform = a sum of sines and cosines of varying amplitudes of multiples of the the fundamental frequency of that waveform. FS is a discrete series approximation.

A Fourier Transform essentially converts a time domain function to its frequency domain components. That is its spectral content. For example the FT of a sine wave would just be a single spike at the given frequency. If the sine wave has harmonics, as in a guitar or piano tone, then the FT would be a series of spikes; one each at the fundamental frequency and 3rd and 5th and 7th etc all with declining amplitudes.
FT is a continuous function approximation.

Last edited: Sep 22, 2011
7. Sep 22, 2011

### quietrain

oh..

so when i integrate over all frequency, does it have to = 1?

8. Sep 22, 2011

### paulfr

No, you are thinking of Probability Density functions. The area under that curve =1

For spectral content, the ENERGY of the spectra must equal the energy calculated from the time domain waveform.

9. Sep 23, 2011

### quietrain

this is confusing

thanks!