The inverse of the continous Fractional Fourier Transform (FrFT)

Question

Foxy Seif Eddine 2013-9-16

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评论： zoubir 2023-2-13

Hello,

I'm trying to use this pre-programmed function of the continuous fractional Fourier transform (FrFT) for 1-D arrays available on this website:

http://nalag.cs.kuleuven.be/research/software/FRFT/

Precisely, the one which is the core of the rest of codes (2D,discret ..etc).

http://nalag.cs.kuleuven.be/research/software/FRFT/frft.m

It takes as entry parameters, a 1-D array to transform i.e: X, and the transform fractional order i.e: a, it works fine for the forward transform

F = FrFT(X,a)

But I couldn't get the inverse transform when I tried to obtain the inverse transform to recover the 1D original array X:

Xr = FrFT(F,-a)

Xr obtained values are completely different from the original X values, can anyone tell me what is wrong here, please?

As far as i know, one of the properties of the FrFT, its inverse is obtained by taking the FrFT of the negatif of its order, i.e FrFT with order -a.

Regards,

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Tzila Ajamian 2017-3-20

Hello Sir, I'm trying to apply the same work that you tried before 4 years. So can you give me some advices from your experience? Did you reach a solution?

Best regards,

Banhi Das 2023-1-11

Please help me with the Code of inverse fractional fourier transform

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Answer 1

Kritika 2014-11-5

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hello sir,

Even I am trying to do the same thing but with a different frft code and its result are not coming correct. If you can help me with it then let me know so that i can share my program with you.

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zoubir 2023-2-13

Hello sir

i have this prb can u help me

Error using .*

Integers can only be combined with integers of the same class, or scalar doubles.

Error in frft (line 31)

fI(m, n) = 1/sqrt(M*N) * sum(sum(I.*exp(-2*pi*1i*((m-1)*U/(M) + (n-1)*V/(N))).*(abs(U/(M))+abs(V/(N)))^alpha));

then i did the double but the same prb

Error using .*

Integers can only be combined with integers of the same class, or scalar doubles.

Error in frft (line 31)

fI(m, n) = 1/sqrt(M*N) * sum(sum(I.*exp(-2*pi*1i*((m-1)*U/(M) + (n-1)*V/(N))).*(double(abs(U/(M))+abs(V/(N))))^alpha));

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Answer 2

Torben Purz 2018-10-11

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https://ww2.mathworks.cn/matlabcentral/answers/87341-the-inverse-of-the-continous-fractional-fourier-transform-frft#answer_340977

Hello, I think I figured out how to fix this without a lot of work. Just add this line:

if (a<0), a = 2+a; end

above the if(a==0) condition. After applying the inverse transform you need to flip your array then. If you think about it, applying first a (FrFT) and then -a (iFrFT) you end up with a "total" a of 2, so you need to flip your end result.

Hope that helps!