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$\DeclareMathOperator{\FFT}{FFT}\DeclareMathOperator{\IFFT}{IFFT}$Assuming I have a matrix $X$ of size $64\times16$. Taking the $\IFFT$ for it in column-wise, I means that $Y = \IFFT(X)$;

Is it possible to get a relationship between every row in $X$ and its corresponding row in $Y$?

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No. Your problem doesn't put any constraints on the columns, so they're totally independent. Then, transforming them to a different base doesn't change that, at all.

If the entries in different columns had nothing to do with other columns, that won't change. The fact that you arranged your data in a matrix doesn't magically allow any operation to introduce relationships that weren't there.

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  • $\begingroup$ I agree, but I have seen this paper. arxiv.org/pdf/1512.06502.pdf Then checked Eq(12). If we put $H_l = I$, that'll mean we got relationship between every row however the ifft was taken column-wise $\endgroup$
    – Fatima_Ali
    May 27, 2020 at 10:33
  • $\begingroup$ That paper takes the FFT in the same dimension as it used the IFFT. Also, uses a channel model that introduces interdependencies. So, very different from the question you ask. $\endgroup$
    – Marcus Müller
    May 27, 2020 at 10:39
  • $\begingroup$ thank you so much Marcus ... $\endgroup$
    – Fatima_Ali
    May 28, 2020 at 1:35

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