For example let's say there are 4 data symbols d(1) to d(4). If I take FFT of the sequence, I get values let's say D(1) to D(4). Now if I include zeros in between each consecutive data (Like the sequence will be D(1),0,D(2),0,D(3),0,D(4),0). Now if I take IFFT of the sequence, I observe a repeating pattern in the output. If output vector is x (x(1)-x(8)), it seems x(1) to x(4) is exactly similar as x(5) to x(8). Is there any particular property of FFT which causes this behavior? I understand that adding zeros in between the data are bringing that repetition, but I am confused how and why. Because when the zeros are added after consecutive data such as D(1),...D(4),0,0,0,0, the output doesn't show such repetition or periodicity.
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3$\begingroup$ Does this answer your question: Sequence expansion by zeros and interpolation - does it insert additional frequencies?. $\endgroup$– Dan BoschenCommented Sep 5 at 2:01
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1$\begingroup$ Looks like this is an oft-asked question. I'm sorta disappointed in some of the teaching and advocacy regarding this issue because there's really no two ways about it, and I'm rather a sorta Nazi (thought police) about it: The Discrete Fourier Transform maps a periodic sequence $x[n]$, having period $N$ to another periodic sequence $X[k]$ having the same period $N$. Doesn't matter if you zero pad or not. $\endgroup$– robert bristow-johnsonCommented Sep 6 at 2:25
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