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Can we construct exact analog signal at receiver as same as the source from the sampled signal?

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closed as unclear what you're asking by Stanley Pawlukiewicz, lennon310, Marcus Müller, Fat32, A_A Oct 26 '18 at 8:48

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  • $\begingroup$ Can you clarify: what is the bandwidth of the transmitted signal; what is the channel; where and at what rate is the signal sampled? $\endgroup$ – MBaz Oct 20 '18 at 15:10
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In theory: No we can not. For a signal to be sampled accurately it needs to be band limited. In order to be band limited it needs to be infinite in time and that doesn't exist.

In practice: sure we can. For any given level of accuracy, signal spectrum and bandwidth of interest it's pretty straight forward to find sampling parameters (rate, bit depth) that will do.

This boils down to your definition of "exact".

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  • $\begingroup$ I think your theory and practice should be inter-changed :-). Just as, in theory brickwall filters do exist, but not in practice, so in theory, there exist bandlimited signals which have infinite duration however; but it's not a problem to sample them though, just as an infinite series summation is computed in theory; i.e, the time duration of the theory is just a mathematical model and not the actual physical time. So exact recovery is possible in theory, but not in practice. Therefore, in practice, an acceptable approximate recovery is performed. $\endgroup$ – Fat32 Oct 20 '18 at 22:54
  • $\begingroup$ @Fat32: nope. Mathematically it's impossible to have a signal that's limited both in time and in frequency. $\endgroup$ – Hilmar Oct 21 '18 at 23:54
  • $\begingroup$ Than how we can hear same speech spoken by remote person without any error ?????? Because our output is distorted And still it gives same speech spoken by remote person please explain if you know I have very hard time to understand this process of signal reconstruction $\endgroup$ – Mehul Dangar Oct 22 '18 at 4:26
  • $\begingroup$ @Hilmar Sorry if my comment was not clear enough. Let me exactly repeat what I stated. In theory a signal can be bandlimited in frequency but then it will be infinite duration in time. Then in theory this signal can be sampled and reconstructed from its infinite samples exactly. This is possible in theory. But in practice since we do not have infinite time, we can only use finite number of samples and therefore the signal will not be exactly bandlimited and have some aliasing distortion.Therefore,in practice exact reconstruction is not possible, but acceptable approximate. $\endgroup$ – Fat32 Oct 22 '18 at 6:35
  • $\begingroup$ Sorry, I misunderstood $\endgroup$ – Hilmar Oct 23 '18 at 5:14

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