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 40m Log Not logged in Message ID: 16360     Entry time: Mon Sep 27 12:12:15 2021     In reply to: 16355     Reply to this: 16361
 Author: Ian MacMillan Type: Summary Category: Computers Subject: Quantization Noise Calculation Summary

I have not been able to figure out a way to make the system that Aaron and I talked about. I'm not even sure it is possible to pull the information out of the information I have in this way. Even the book uses a comparison to a high precision filter as a way to calculate the quantization noise:

"Quantization noise in digital filters can be studied in simulation by comparing the behavior of the actual quantized digital filter with that of a refrence digital filter having the same structure but whose numerical calculations are done extremely accurately."
-Quantization Noise by Bernard Widrow and Istvan Kollar (pg. 416)

Thus I will use a technique closer to that used in Den Martynov's thesis (see appendix B starting on page 171). A summary of my understanding of his method is given here:

A filter is given raw unfiltered gaussian data  then it is filtered and the result is the filtered data  thus we get the result:   where  is the raw noise filtered through an ideal filter and  is the difference which in this case is the quantization noise. Thus I will input about 100-1000 seconds of the same white noise into a 32-bit and a 64-bit filter. (hopefully, I can increase the more precise one to 128 bit in the future) then I record their outputs and subtract the from each other. this should give us the Quantization error :

and since  because they are both running through ideal filters:

and since in this case, we are assuming that the higher bit-rate process is essentially noiseless we get the Quantization noise .

If we make some assumptions, then we can actually calculate a more precise version of the quantization noise:

"Since aLIGO CDS system uses double precision format, quantization noise is extrapolated assuming that it scales with mantissa length"
-Denis Martynov's Thesis (pg. 173)

From this assumption, we can say that the noise difference between the 32-bit and 64-bit filter outputs:    is proportional to the difference between their mantissa length. by averaging over many different bit lengths, we can estimate a better quantization noise number.

I am building the code to do this in this file

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