[SciPy-User] Help with fast fourier transform
Chris Michalski
chris.michalski@gmail....
Thu Apr 29 23:06:56 CDT 2010
Looks like your problem is one of expectations.
You did an FFT on real data - specifically a "pulse" that is 100 point long surrounded by 450 "zeros" on either side. Since the FFT function computes a complex FFT - you got negative and positive frequencies. As the FFT samples come out, they represent "DC" (zero freq) through just shy of fs/2 (fs = sample rate), then the output wraps to -fs/2 which then advances to just shy of "0".
Your original output is correct - it just needs to be reordered. The "desired" output you referenced (the picture) takes the last "N/2" complex points from the FFT function and moves then to the first N/s points. Once the data is reordered, before you plot you have to set the frequency resolution of the FFT. In a complex FFT output, the first sample in the reordered output would correspond to -fs/2 and the uppermost frequency would be (about fs/2) The complication is that there is a zero frequency (DC offset) term. Since the FFT returns an even number of samples (specifically a power of two), the convention I remember is that there are more "negative frequency" samples than positive frequency samples.
By the way. There is a much simpler way to get a pulse, specifically:
import numpy as np
f = np.zeros(1000, dtype='d')
f[450:550] = 1.0
If "F" is the FFT of "f" (the time function), then the reordering can be accomplished with
# Create new array to hold the reordered output (holding complex data)
size = len(F)
FF = np.array(size, dtype='D')
FF[0:size/2] = F[size/2:]
FF[size/2+1:] = F[0:size/2]
Getting the hang of thinking of operations as vectored code rather than loops can take some practice - but well worth the results.
chris
On Apr 29, 2010, at 9:17 AM, Oscar Gerardo Lazo Arjona wrote:
> Hello! I'm new to this mailing list and to numpy in general.
> I need to calculate fft for my optics class. But I'm having trouble.
>
> This is the code I'm using (commented):
>
> import pylab
> import numpy as np
>
> def g(x):
> if x>450 and x<550:
> return 1
> else:
> return 0
> f=[g(x) for x in range(0,1000)]
> f=np.array(f)
>
> #this funtion can be ploted as
> #http://i41.tinypic.com/k0shnk.png
> #which is a step function "centered" at 500
>
>
> F=np.fft.fft(f)
> #when calculate the fft of f i get an array of complex numbers
> #whose absolute value can be ploted as
> #http://i40.tinypic.com/1zcecxx.png
>
> #But that is not the desired output.
> #Instead of that i expect something that can be ploted like this
> #http://i39.tinypic.com/1zmch0g.png
>
>
> #what i think must be happening because my function f
> #has an offset of 500 (it's supposed to be centereed at 500)
>
> #So i think it all reduces to two options:
> #somehow telling fft to consider the origin at 500
> #(indicate thetell the offset)
>
> #Or make fft accept a list of points like
> #[[-2,0],[-1,1],[0,1],[1,1],[2,0]]
> #so that it can know the position of the step relative to the origin
>
> Please help!
>
> Oscar
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