# Fourier Analysis

Discussion in 'General Electronics Chat' started by electron_prince, Apr 16, 2013.

1. ### electron_prince Thread Starter Member

Sep 19, 2012
93
3
Hi,
I have never enjoyed playing with Fourier transform but now as I am forced to learn it, I came with several doubts. And perhaps you'd be able to clear them.

1) So, Fourier analysis says that we can express any periodic signal as a linear combination of harmonically related complex exponentials (or perhaps sinusoids). And if my system is linear then the output of my system will also be a linear combination of the associated outputs.

2) On the other hand, complex exponentials are eigen function for LTI systems. So if we put a complex exponential as an input to an LTI system, we'll get the same complex exponential out of the system multiplied by a complex function in frequency, called the frequency response.

so $e^{jk\omega}$ produce H($\omega$).$e^{jk\omega}$

and $a_{k}.e^{jk\omega}$ will produce $a_{k}.H(\omega).e^{jk\omega}$

where $a_{k}$ is the fourier series coefficient.

does it mean that fourier series tells about the scale factor for the input complex exponential at a given frequency and frequency response tells the scale factor for the output at given frequency?

second, is a square wave a bandlimited signal? To me it doesn't look like a bandlimited signal because to make for the discontinuity, we need more and more and more sinusoidal signals with higher frequency. So the scale factor for the harmonically related input complex exponentials are never approaching zero. am i right?

2. ### Veracohr Well-Known Member

Jan 3, 2011
559
77
If I understand your question correctly: yes. The Fourier series describes the signal, and the complex coefficient of each frequency is a "scale factor" for that frequency.

You're right. A true, theoretical (ie. not real) square wave will have frequency components extending to infinity. A real one will of course be limited by physical component limitations.