Monday, August 27, 2018

fft - Precision measurement of sine wave amplitude with ADC


I want to measure amplitude of a sine wave input precisely with a limited resolution ADC.


As an example suppose that I have $1\textrm{ MHz}$ pure sine wave input to the $320\textrm{ Msps}$ $10$-bit ADC. I beleived there is many redundancy in data and with some signal processing I could get more Precision than $10$-bit.


Is there any way that I can do this without any change in circuit, like adding noise or other hardware change?



Answer



A sine wave has infinitesimally little bandwidth. By rotating, filtering appropriately and decimating, you can reduce the sample rate very much.


Each of these filtering operations is typically a summing operation, in which you "average" out noise (which isn't your main concern), but also get a more precise estimate for the amplitude.



Decimation in DSP is very commonly done. You'd probably want to do that anyway – 320 MS/s is really no fun to deal with, and you don't need that bandwidth.


Of course, you can also correlate with a synthesized sine, and measure the correlation coefficient to get the power/amplitude.


Other options are things like proper spectral estimators – there's a lot to choose from, including Welch's method, or Pisarenko-based approaches. Especially if your signal is noisy, these might be interesting, but it really depends a lot on what exactly you're measuring and how you model your noise.


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