# Fourier Transform Doubt!

1. Mar 24, 2012

### salil87

Hi
Do Fourier Transforms give us actual amplitude/phase of the particular frequency (ejωt) just like Fourier series?
Thanks
Salil

2. Mar 24, 2012

### rbj

sorta, yes. but the inverse continuous Fourier transform is an integral not a summation like in the Fourier series. so the actual amplitude is proportional to the product of $X(f)$ and the width of the sliver of spectrum $df$.

to compare, give the (inverse) Fourier integral a finite width (with the limits of the integral) and then represent that finite width integral with a Riemann summation and then you will be able to see the relationship between the inverse Fourier transform and the Fourier series. in a loose sense, they are the same thing.

3. Mar 26, 2012

### sophiecentaur

The series is a Discrete process where the Transform is Continuous. The series can yield 'wrong' / misleading results if you ignore the basic rules.

4. Mar 31, 2012

### Anitha Sankar

what is the fourier transform of sum( Vhcos(hwt)) where h varies from 1 to infinity

5. Mar 31, 2012

### sophiecentaur

Hi
I assume that when you write Vh , the h is a suffix.
The transform will be a regular 'comb' of components at frequency w, hw, 2hw etc. with amplitdes given by the coefficients V. In fact, the original function is of a form that tells you the frequency spectrum just by 'observation'.

6. Mar 31, 2012

### Cecilia48

http://www.infoocean.info/avatar2.jpg [Broken]The series is a Discrete process where the Transform is Continuous.

Last edited by a moderator: May 5, 2017
7. Apr 1, 2012

### sophiecentaur

I guess I meant "sum' as against 'integral'.
Is that better?

Last edited: Apr 1, 2012