How do I invert nested functions in MATLAB?

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If I have a variable (let's call it a) and then I apply the following multiple functions to transform it into a second variable, (b), how would I reverse it?
b = fftshift(fftn(fftshift(a)));
I tried doing the following:
c = ifftshift(ifftn(ifftshift(b)));
If this had worked, c would have been equal to a (the initial, non-transformed data set). Why doesn't it? Is there a better, more universal way of reversing the function initially applied to A? I tried finverse, but it didn't work in the way I used it because fftshift works on doubles, and I was using a sym-type variable when I tried getting the inverse.
Any help is appreciated

Accepted Answer

KALYAN ACHARJYA
KALYAN ACHARJYA on 14 Aug 2019
Edited: KALYAN ACHARJYA on 14 Aug 2019
"If I have a variable (let's call it a) and then I apply the following multiple functions to transform it into a second variable, (b), how would I reverse it?"
a=magic(3)
b = fftshift(fftn(fftshift(a)));
c = ifftshift(ifftn(ifftshift(b)))
Result:
a =
8 1 6
3 5 7
4 9 2
c =
8.0000 1.0000 6.0000
3.0000 5.0000 7.0000
4.0000 9.0000 2.0000
  3 Comments
Walter Roberson
Walter Roberson on 14 Aug 2019
Edited: Walter Roberson on 15 Aug 2019
Floating point roundoff. I suggest that you subtract the two versions and look at the difference.
fft involves the use of transcendental trig functions, so in order for the inverse to be always bit for bit exact, you would need to use indefinite precision.
You can use counting arguments to prove that if you use finite floating point that asin(sin(x)) cannot always exactly equal x even within the primary period.
Ak K
Ak K on 15 Aug 2019
Got it, thanks; I tried that, and the difference was indeed extremely small.

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