DAC interpolation 
DAC interpolation 
Mar 2 2013, 03:25
Post
#1


Group: Members Posts: 2 Joined: 2March 13 Member No.: 106971 
The NyquistShannon theorem (the sampling theorem) states that if a function x(t) contains no frequencies greater than B hertz, it is completely characterized by measuring its amplitudes at a series of points spaced 1/(2B) seconds apart. It further states that to reconstruct the original signal one must use the WhittakerShannon interpolation theorem, computing the sum of the infinite series of normalized sinc functions for each sample. (Well,
CODE $x(t)=\sum_{\infty}^{\infty}x[n]\cdot{\rm sinc}(\frac{tnT}{T})$ where n is the sample number, t is the sample time, T is 1/(sampling rate), and sinc(x) is the normalized sinc function.)I've never (in my somewhat limited experience) seen an audio DAC that does that, yet they seem to have pretty reasonable output. How accurate are the standard approximations, really? What is the interpolation error? How does one characterize it? 


Mar 2 2013, 11:11
Post
#2


Group: Members Posts: 422 Joined: 16December 10 From: Palermo Member No.: 86562 
Consider that in strict theory the Shannon theorem conditions never apply in reality simply because mathematically a band limited signal cannot be also time limited, thus "having an infinite number of samples, etc etc...".
In real world, with a sufficiently large number of samples, as Alexey Lukin said, the truncation error rounds toward zero and other components (quantization, sampling time uncertainty etc...) prevail. This post has been edited by Nessuno: Mar 2 2013, 11:12  ... I live by long distance.



LoFi Version  Time is now: 20th August 2014  12:17 