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Signal Processing

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    $\begingroup$ Please have a look at how I made your post readable. Please use Latex formatting for formulas so people can actually understand what you're asking. Another thing: this is a typical homework problem, so please show us what you did and where you're stuck. $\endgroup$ Commented Jan 20, 2018 at 16:28
  • $\begingroup$ There is a thing called Direct Proof for which you can use specific properties of the dft to start from the left and end on the right. Do you think you could have a go at this and then update the question with your progress? As this is a homework question, at the moment, it does not contain any work you may have done so far and therefore it is unclear what exactly you are stuck with (?) $\endgroup$ Commented Jan 20, 2018 at 23:18
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    $\begingroup$ the result you seek appears to be true only if $x[n]$ is real. $\endgroup$ Commented Mar 1, 2018 at 9:07
  • $\begingroup$ how the result is true if $x[n]$ is real ? please explain.... @robert bristow-johnson $\endgroup$ Commented Mar 1, 2018 at 16:03
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    $\begingroup$ if $x[n]$ is purely real (that is $\Im\{x[n]\}=0 \quad \forall n \in \mathbb{Z}$), then $X[-k]=X^*[k]$ and likewise $X[k]=X^*[-k]$ and that bottom "$\ne$" becomes "$=$". $\endgroup$ Commented Mar 1, 2018 at 18:18