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 Mon Sep 20 15:42:44 2021, Ian MacMillan, Summary, Computers, Quantization Code Summary Wed Sep 22 14:22:35 2021, Ian MacMillan, Summary, Computers, Quantization Noise Calculation Summary Mon Sep 27 12:12:15 2021, Ian MacMillan, Summary, Computers, Quantization Noise Calculation Summary Mon Sep 27 16:03:15 2021, Ian MacMillan, Summary, Computers, Quantization Noise Calculation Summary Mon Sep 27 17:04:43 2021, rana, Summary, Computers, Quantization Noise Calculation Summary Thu Sep 30 11:46:33 2021, Ian MacMillan, Summary, Computers, Quantization Noise Calculation Summary Wed Nov 24 11:02:23 2021, Ian MacMillan, Summary, Computers, Quantization Noise Calculation Summary Wed Nov 24 13:44:19 2021, rana, Summary, Computers, Quantization Noise Calculation Summary Tue Dec 7 10:55:25 2021, Ian MacMillan, Summary, Computers, Quantization Noise Calculation Summary Fri Dec 10 13:02:47 2021, Ian MacMillan, Summary, Computers, Quantization Noise Calculation Summary Mon May 9 15:32:14 2022, Ian MacMillan, Summary, Computers, Quantization Noise Calculation Summary Fri Sep 2 13:30:25 2022, Ian MacMillan, Summary, Computers, Quantization Noise Calculation Summary
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 $f(t)$ then it is filtered and the result is the filtered data $x(t)$ thus we get the result: $f(t)\rightarrow x(t)=x_N(t)+x_q(t)$  where $x_N(t)$ is the raw noise filtered through an ideal filter and $x_q(t)$ 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 $e(t)$:
$e(t)=x_{32}(t)-x_{64}(t)=x_{N_{32}}(t)+x_{q_{32}}(t) - x_{N_{64}}(t)-x_{q_{64}}(t)$
and since $x_{N_{32}}(t)=x_{N_{64}}(t)$ because they are both running through ideal filters:
$e(t)=x_{N}(t)+x_{q_{32}}(t) - x_{N}(t)-x_{q_{64}}(t)$
$e(t)=x_{q_{32}}(t) -x_{q_{64}}(t)$
and since in this case, we are assuming that the higher bit-rate process is essentially noiseless we get the Quantization noise $x_{q_{32}}(t)$.

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:  $x_{q_{32}}(t)-x_{q_{64}}(t)$  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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