Equivalence of ratios of transforms

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JOB
JOB 2020-2-11
回答： JOB 2020-2-12
Please help me out on this, The evaluvation of IFFT(x)/IFFT(y) and FFT(x)/FFT(y), are giving the same answer regardless of the size or nature (real or complex) of x or y. Is this any special property of FFT/IFFT transforms? Please let me know if there are any references regarding this.
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Star Strider
Star Strider 2020-2-11
I would not expect them to be different.
The Fourier and inverse Fourier transforms are linear transforms:
and:
so the energies of the transforms of the functions remain the same.

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JOB
JOB 2020-2-12
Thank you, for sparing your valuable time for clearing the doubt. Are there any references where this type of identies are given with proof?

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