[Numpy-discussion] FFT and reconstruct

[Feng Yu]

Hi Vasco,

It looks slightly strange that you are using cos instead of exp in the
reconstruction of the signal.

I'd recommend you take a look at
http://docs.scipy.org/doc/numpy-1.10.1/reference/routines.fft.html

Also the documents of fftfreq, fftshift, and ifft.

Best,

- Yu

On Sat, May 14, 2016 at 6:27 AM, Vasco Gervasi <yellowhat46 at gmail.com>
wrote:

> Hi all,
> I am trying to understand how FFT work, so I wrote the attached script.
> The idea is to extract amplitude and phase of a signal and then
> reconstruct using amplitude and phase information.
> As you can see, I create some cosine curve on the interval t0-t1.
> Let's start with t0=1.0 and t1=3.0 and consider just y['1']
> = cos(1.0*omega*t), the signal is.
> [image: Immagine incorporata 1]
> The amplitude and phase for each order are:
> [image: Immagine incorporata 2]
> But if I try to reconstruct the signal using amplitude and phase:
> [image: Immagine incorporata 3]
> So as you can see there is a shifting of 180 deg.
>
> Now let's consider another case, t0=2 and t1=3, the signal is
> y['Signal'] = 1.0*cos(1.0*omega*t) + 2.0*cos(2.0*omega*t) +
> 3.0*cos(3.0*omega*t + pi/4) + 4.0*cos(4.0*omega*t) + 5.0*cos(5.0*omega*t) +
> 1.0
> The reconstructed signal is very similar to the initial one:
> [image: Immagine incorporata 4]
> but is not exactly the same.
> Any advice?
>
> Thanks
>
>
>
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