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I sampled a signal and unfortunately every second sample is very noisy. The noise is Gaussian and bandlimited exactly in the same bandwidth as my signal. Is there a way to improve the noise without averaging? I need to keep the original sample rate.

In theory I know the spectrum of my signal. I can skip all noisy (every second) samples and do a FFT. This gives me a spectrum with very low noise. But it is undersampled.

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    $\begingroup$ That's a peculiar setup. Do you know the phenomenon that is causing the noise to occur on such a schedule? Note that if the noise is only present in every other sample, and it covers the same bandwidth as your original signal, then it also is undersampled. Because of the dual phenomenon to the one I refer to here, the spectrum of the noise signal should actually be replicated twice in the frequency domain. $\endgroup$ – Jason R Sep 7 '16 at 2:14
  • $\begingroup$ Can you describe the data source and signal processing that leads to this? Some detail might explain what you are doing. I presume that the effect you mention is not intentional! In addition, a link to some of the actual data might be helpful. $\endgroup$ – rrogers Sep 13 '16 at 17:37

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