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Entry  Mon Sep 20 15:42:44 2021, Ian MacMillan, Summary, Computers, Quantization Code Summary 472px-Typical_State_Space_model.svg.pngBiquad_filter_DF-IIx.svg.pngSS-IIR-TF.pdf
    Reply  Wed Sep 22 14:22:35 2021, Ian MacMillan, Summary, Computers, Quantization Noise Calculation Summary IIR64-bitnoisespectrum.pdf
       Reply  Mon Sep 27 12:12:15 2021, Ian MacMillan, Summary, Computers, Quantization Noise Calculation Summary 
          Reply  Mon Sep 27 16:03:15 2021, Ian MacMillan, Summary, Computers, Quantization Noise Calculation Summary DeltaNoiseSpectrum.pdf
             Reply  Mon Sep 27 17:04:43 2021, rana, Summary, Computers, Quantization Noise Calculation Summary 
                Reply  Thu Sep 30 11:46:33 2021, Ian MacMillan, Summary, Computers, Quantization Noise Calculation Summary SS-IIR-Bode.pdfPSD_32bit.pdfPSD_64bit.pdf
                   Reply  Wed Nov 24 11:02:23 2021, Ian MacMillan, Summary, Computers, Quantization Noise Calculation Summary PSD_IIR_all.pdf
                      Reply  Wed Nov 24 13:44:19 2021, rana, Summary, Computers, Quantization Noise Calculation Summary 
                         Reply  Tue Dec 7 10:55:25 2021, Ian MacMillan, Summary, Computers, Quantization Noise Calculation Summary DF2_TS.pdfBIQ_TS.pdfScreen_Shot_2021-12-07_at_11.47.57_AM.pngPSD_COMP_BIQ_DF2.pdfPSD_COMP_SS_DF2.pdf
                            Reply  Fri Dec 10 13:02:47 2021, Ian MacMillan, Summary, Computers, Quantization Noise Calculation Summary G0900928-v1_(dragged).pdfPSD_COMP_BIQ_DF2.pdfInput_PSD.pdfInput_Filter.pdfQuantizationN.zip
                               Reply  Mon May 9 15:32:14 2022, Ian MacMillan, Summary, Computers, Quantization Noise Calculation Summary SUS-ETMX_SUSYAW3_0.0.pdfLowNoiseBiquad2.pdfquant_noise_floor.pdf
Message ID: 16498     Entry time: Fri Dec 10 13:02:47 2021     In reply to: 16492     Reply to this: 16836
Author: Ian MacMillan 
Type: Summary 
Category: Computers 
Subject: Quantization Noise Calculation Summary 

I am trying to replicate the simulation done by Matt Evans in his presentation  (see Attachment 1 for the slide in particular). 

He defines his input as x_{\mathrm{in}}=sin(2\pi t)+10^{-9} sin(2\pi t f_s/4) so he has two inputs one of amplitude 1 at 1 Hz and one of amplitude 10^-9 at 1/4th the sampling frequency  in this case: 4096 Hz

For his filter, he uses a fourth-order notch filter. To achieve this filter I cascaded two second-order notch filters (signal.iirnotch) both with locations at 1 Hz and quality factors of 1 and 1e6. as specified in slide 13 of his presentation

I used the same procedure outlined here. My results are posted below in attachment 2.

Analysis of results:

As we can see from the results posted below the results don't match. there are a few problems that I noticed that may give us some idea of what went wrong.

First, there is a peak in the noise around 35 Hz. this peak is not shown at all in Matt's results and may indicate that something is inconsistent.

the second thing is that there is no peak at 4096 Hz. This is clearly shown in Matt's slides and it is shown in the input spectrum so it is strange that it does not appear in the output.

My first thought was that the 4kHz signal was being entered at about 35Hz but even when you remove the 4kHz signal from the input it is still there. The spectrum of the input shown in Attachment 3 shows no features at ~35Hz.

The Input filter, Shown in attachment 4 shows the input filter, which also has no features at ~35Hz. Seeing how the input has no features at ~35Hz and the filter has no features at ~35Hz there must be either some sort of quantization noise feature there or more likely there is some sort of sampling effect or some effect of the calculation.

To figure out what is causing this I will continue to change things in the model until I find what is controlling it. 

I have included a Zip file that includes all the necessary files to recreate these plots and results.

Attachment 1: G0900928-v1_(dragged).pdf  52 kB  | Hide | Hide all
G0900928-v1_(dragged).pdf
Attachment 2: PSD_COMP_BIQ_DF2.pdf  267 kB  | Hide | Hide all
PSD_COMP_BIQ_DF2.pdf
Attachment 3: Input_PSD.pdf  52 kB  | Hide | Hide all
Input_PSD.pdf
Attachment 4: Input_Filter.pdf  15 kB  | Hide | Hide all
Input_Filter.pdf
Attachment 5: QuantizationN.zip  211 kB  Uploaded Fri Dec 10 14:03:29 2021
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