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Inverse Fourier Transform

06/04/2017 11:41 AM

Hi friends. İ have freq(Hz)-ampitude values and I want to plot time (s)-acceleration graph.how can I do this with using inverse Fourier function on excel?

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#1

Re: inverse fourier transform

06/04/2017 2:38 PM

You cannot convert back to time series unless you also have phase information.

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#2
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Re: inverse fourier transform

06/04/2017 2:43 PM

How can I calculate phase? Can you help me?

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#8
In reply to #2

Re: inverse fourier transform

06/04/2017 5:45 PM

You cannot calculate phase from the amplitude spectrum. Let me explain with an example.

Say you have 1024 data samples. You run it through an FFT and get 1024 complex frequency values, i.e. 1024 real and 1024 imaginary values.

If you now take these complex frequency values through an inverse FFT, you would get your original 1024 sample time series.

To get the amplitude spectrum (which you have) you square each real and imaginary, add them, and take the square root. amplitude = sqrt(real2 + imag2). But from the amplitude spectrum, you cannot go back to get the real and imaginary components to do the inverse FFT.

To get the phase spectrum, you need the real and imaginary frequency components. phase = arctan(imaginary/real).

If you have both the amplitude spectrum and the phase spectrum, you could combine these to recreate the real and imaginary frequency components.

real = amplitude x cos(phase), imag = amplitude x sin(phase)

You could then run the inverse FFT to get back to time series.

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#9
In reply to #8

Re: inverse fourier transform

06/04/2017 5:51 PM

Mr. Rixter can you send me an example xls file about your explains?

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#3

Re: inverse fourier transform

06/04/2017 2:45 PM

..." In Excel, on the "Fourier Analysis" window, select "Inverse" on the

bottom of the window. "...

https://www.pcreview.co.uk/threads/inverse-fft.3827301/

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#4
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Re: inverse fourier transform

06/04/2017 2:50 PM

I got inverse FFT of amplitude and I had complex numbers. How can I find acceleration in time by complex numbers ?

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#5
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Re: inverse fourier transform

06/04/2017 2:59 PM
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#6
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Re: inverse fourier transform

06/04/2017 3:22 PM

I mean I want to get "M" column from "K" column and plottime-acceleration-2graph in data as shown in this picture. How can I do that ?

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#7
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Re: inverse fourier transform

06/04/2017 3:54 PM
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#10
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Re: inverse fourier transform

06/04/2017 6:01 PM

No, nothing you do to your amplitude spectrum will recover lost information. See #8. When you combine real and imaginary to get amplitude, you only have half of the information.

It's synonymous to distance and direction. Think of real as north-south and imaginary as east-west. If real is 3 miles and imaginary is 4 miles, distance is 5 miles. But if you only know distance is 5 miles and don't know the direction, you can't find north-south or east-west.

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#11
In reply to #10

Re: inverse fourier transform

06/04/2017 6:05 PM

http://dosya.co/a7e53b8akm4n/data.xlsx.html

This is my xls file

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#12
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Re: inverse fourier transform

06/04/2017 6:08 PM
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#13
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Re: inverse fourier transform

06/05/2017 8:35 AM

Anyone fancy doing a Fourier analysis of either the red line or blue line?

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#15
In reply to #13

Re: inverse fourier transform

06/05/2017 3:25 PM

Answer: Pig DNA

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#16
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Re: inverse fourier transform

06/05/2017 6:24 PM

I'll pass that on to my fellow church bellringers For the record, it is actually a standard "method" (piece of bellringing music) with the title of Cambridge Surprise Minor.

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#18
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Re: inverse fourier transform

06/06/2017 10:15 AM

To me, it is still pig DNA, or might as well be. I can't read bell-ringer music.

Why isn't that already automated? We want to automate everything else....just kidding.

BTW, are we talking about those who stand at a table with bells and ring out songs or those who pull on the ropes linked to the belfry?

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#19
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Re: inverse fourier transform

06/06/2017 11:39 AM

Automation? Think of the parallel with an orchestra. We could automate that just as easily as a band of church bellringers, but it is actually an occupation where people meet and cooperate.

Church bell ringers stand in a belfry and pull ropes. The "music" is "change ringing" as in the piggy diagram, or "call changes."

Handbell ringers sit or stand with bells in their hands. Unlike church bell ringers, who almost invariably pull only one rope, handbell ringers generally have one in each hand. The music may be change ringing but is more often "proper" music.

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#20
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Re: inverse fourier transform

06/06/2017 12:31 PM

I wanna hear: "Rollover Beethoven."

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#21
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Re: inverse fourier transform

06/06/2017 6:51 PM

Just like ringin' a bell....

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#17
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Re: inverse fourier transform

06/06/2017 1:40 AM

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#14

Re: Inverse Fourier Transform

06/05/2017 12:28 PM

As many have pointed out, one cannot perform an inverse Fourier transform to return to the time domain from just the amplitude information. You also forgot to identify if this amplitude data is positional or velocity information.

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#23
In reply to #14

Re: Inverse Fourier Transform

06/08/2017 12:00 PM

I think I recall that Microsoft Excel FFT produces frequency and phase information columns, but I still would not count on any fidelity in the reverse transform.

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#22

Re: Inverse Fourier Transform

06/08/2017 12:08 AM

Thanks friends for your help.

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