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I have a sample of a signal lets say 8 values of a 16 value sequence. I am trying to obtain the full DFT from the partial.

I am thinking that I am going to work back, I read the matlab documentation and have come acrosss an inverse function. Am I on the right track? I was not able to see a pattern in the results..

yt = [5 2-5i -11.8 + 1.8i 12.85 +1.2i -1-3.4i 0.5-0.866i 6-1.9i 12.8+5i];
ifft(yt);
Xsym = ifft(yt,'symmetric')

Xsym =

    1.2333   -0.7580    2.7979    5.5777   -2.3988   -4.1984    3.4223    0.5402   -1.2162

If I am not on the right track what should I be looking at?

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  • $\begingroup$ I am not sure I follow---if you have a signal of 8 time domain values, the DFT will have 8 frequency domain values, given as fft(yt). What does partial mean? ifft will then recover the time domain values back from the frequency domain values. $\endgroup$ Feb 22, 2023 at 6:33
  • $\begingroup$ The signal has a total of 16 real values, I am required to determine the remaining 8 given these first 8 values. I used the word partial as 8 values are a partial sample of a 16 value sequence. $\endgroup$
    – Tam
    Feb 22, 2023 at 6:45
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    $\begingroup$ The values you're showing (assuming it's yt?) aren't real, they're complex. If that's the first 8 values of a DFT sequence, and you're asked to find the remaining 8, and you know the input is a real sequence, I suggest you learn about the properties of the DFT for real-valued sequences (specifically, conjugate symmetry). If I'm missing the point, then that means your question is still un-clear and you should edit it with more precise information on your problem. $\endgroup$
    – Jdip
    Feb 22, 2023 at 7:07

1 Answer 1

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Sorry if this is indirect. There are requisite study areas for the Fourier Transform and the FFT behind the posted question. Here are suggested study topics:

Review what the Fourier Transform is for real signals, be sure to include both negative and positive frequencies. Start with the simple case of a sinusoid. This can help: https://dsp.stackexchange.com/a/85273/21048

Review how this same function would look in a DFT (the FFT is an algorithm that computes the DFT): Representation of Sampling Frequency in the Fast Fourier transform

From this you will learn the key properties of "negative" and "positive" frequencies in the Fourier Transform specific to real signals, and which bins in the DFT are also considered "negative" and "positive" frequencies. You will learn there is redundancy such that only the positive frequency components need to be kept, as we can derive the negative frequency components from the positive ones.

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