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I am trying to improve the dynamic range of an ADC, by using a second ADC which is the original signal attenuated by a known amount (\$x\$ dB).

So the two signals could be approximated (ignoring any phase differences):
\$y_1(t) = A\sin(\omega t)\$
\$y_2(t) = y_1(t)\$ attenuated by \$x\$ dB

I originally thought about solving this problem by using a 'stacked ADC' approach, which would be to have both signals be analysed and to choose the output of the adc which has not saturated.

However given that the frequency and attenuation of the waves would be a known quantity, would it be possible to combine or 'stitch' these waveforms together into one waveform mathematically by post-processing, and improve the dynamic range that way?

The problem was put to me by my professor but I'm at a loss as to how I would go about it.

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Just to be clear, 10 dB is not the same as 10X so please clarify. Also having increased DR is a little ambiguous it is simply the ratio of max to min, so you can increase max, decrease min or both. IS there some other criteria? – placeholder Feb 27 '13 at 0:32
In this case it will be, since 10dB drop the second signal will mean the second signal will be 0.1 of the first signal. If there was a 20dB drop then the amplitude of the second signal will be 0.01 that of the first (sss-mag.com/db.html). No other criteria, though I'm not sure what you mean by this second part. I'm just attempting to use 2 adc's to increase the DR of one signal by stitching together two waveforms. Each ADC will have a different max and min and I would like to combine these, if it is feasible. – user19475 Feb 27 '13 at 2:21
You just contradicted what you wrote in your OP, see y2 above. – placeholder Feb 27 '13 at 2:34
I really don't see how. If I attenuate y1 by 20dB, then y2 will equal 0.01*y1 (or 100 times drop in the power). What I wrote in the OP was 10dB drop where y2 will equal 0.1*y1 (or 10 times drop in the power). Is that wrong? – user19475 Feb 27 '13 at 2:47
There's also a question about how little noise you can get on the original input signal - no point measuring down to 1 fkteenth of a gnat's hair if the noise is accounting for the lower N bits of your measurement. Search Linear Technology's website for appnotes by Bob Pease & Jim Williams, they wrote some magnificent stuff about low-noise measurement etc. (generally, anything they wrote is worth a read) – John U Feb 27 '13 at 9:05

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