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In signal processing noise can be considered random unwanted data without meaning.

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deconvolution in frequncy vs in time for sparse \ smooth signals

Now, I can either deconvolve in time or in frequency to obtain the frequency content using $L1$ or $L2$ norm minimization , and if there is infinite sampling and no noise the answer is the same. … However, there is time dependent noise, and also a finite measuring time (or it is always a bandwidth-limited signal). …