I have a discrete signal that can only take two values - 0 and 1. Signal is band limited with limiting frequency 1MHz. I sample this signal with frequency 1KHz. Question - can I do better than nearest-neighbor reconstruction or zero-order hold reconstruction? Bonus question: what type of information can be used to increase reconstruction accuracy (other than increasing sampling frequency, obviously)?
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1I think you should put this question here https://dsp.stackexchange.com/ – David Aug 12 '18 at 05:49
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A qualitative signal recovery is possible provided that its parametric model is known. In this case, the quality of signal recovery will be determined by the accuracy of restoring its parameters and that part of the original signal that is not taken into account in the model.
In this case, the reconstruction methods can be different: spectral analysis, the method of least entropy, polynomial regression analysis, and others.
Yuri Negometyanov
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Will it be fruitful to use 1KHz samples to try to reconstruct signal's parametric model and then use this model to reconstruct the signal itself? It feels like I'll get same reconstruction as nearest-neighbor in the end anyway... – wonder.mice Aug 13 '18 at 17:12
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@wonder.mice It totally depends on the signal model. In particular, one can expect a good recovery of frequency-separated low-frequency signals (including modulated signals) or known noise-like codes. The main thing is that the change in the frequency range and the selected sampling amplitude do not completely mask the signal parameters, – Yuri Negometyanov Aug 13 '18 at 17:28
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if the signal is bandlimited to 1 MHz, there is no way that sampling at 1 kHz suffices to get any information. the signal would have to be bandlimited to below 500 Hz in order for sampling with 1000 samples per second to suffice.
this is standard Nyquist-Shannon sampling theorem.
Aloizio Macedo
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