# Chapter 1 - DAC question on reconstruction filter | FX Book Questions | Forum

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Chapter 1 - DAC question on reconstruction filter
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July 12, 2017 - 4:10 pm
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So in the book under chapter 1, the reconstruction of the signal involves passing the signal through a low-pass filter AKA 'reconstruction filter'. . .

"The output filter is called the reconstruction filter and is responsible for re-creating the seemingly missing information that the original sampling operation did not acquire - all the inter-sample fluctuations"

Ok, so wait here one sec! How do we re-create the intersample fluctuations, if we didnt have that information to start with???? Sersiously whats going on here? Maybe i'm just thinking about this too much, but my reasoning is thus:

Say, we have a signal which consists of many complex waveforms. Our sampling fequency is 44,100Khz, so we can aquire and quantize the signal at 22.7 microseconds. What if the signal had fluctuated inbetween those sampling intervals, and when we recreate say, the middle of a particular intersample fluctuation, the real sample is 0.876 (for example) but our 'averaging' done with each sample (with the sin(x)/x function) will really average out between the two quantized samples (of which the intersample part inbetween we are looking at) and spit out a value as such.Â  How then can we re-create this accurately? Surely if intersample 'signals' are in fact higher than nyquist in frequency, we cant hear them but they effect the signal as well, if they were below nyquist we would sample them?

July 13, 2017 - 10:17 am
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Ok, so wait here one sec! How do we re-create the intersample fluctuations, if we didnt have that information to start with???? Sersiously whats going on here? Maybe i'm just thinking about this too much, but my reasoning is thus:

This was the same kind of argument Nyquist faced, and is the founding basis for digital audio and why it actually works - and yes we can recover the missing intersample fluctuations that weren't sampled. See Figure 1.5 which graphically displays how the signal is reconstructed, with the time-domain sinc() functions adding up to recreate the missing intersample fluctuations as a result of convolution with the output LPF. Google it and you'll find a zillion papers about it. Here's a pretty good one:

http://www.spot.pcc.edu/~ghech.....cument.pdf

- Will

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July 13, 2017 - 4:37 pm
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Thanks Will, I will take a look at that paper!

August 26, 2017 - 5:28 pm
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Here's another excellent resource by Nigel Redmond:

http://www.earlevel.com/main/t.....?order=asc

- Will

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