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File:Frequency spectrum of a sinusoid and its quantization noise floor.gif

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Summary

Description
English: This is a comparison of quantizing a sinusoid to 64 levels (6 bits) and 256 levels (8 bits). The additive noise created by 6-bit quantization is 12 dB greater than the noise created by 8-bit quantization. When the spectral distribution is flat, as in this example, the 12 dB difference manifests as a measurable difference in the noise floors.
Date
Source Own work
Author Bob K
Permission
(Reusing this file)
I, the copyright holder of this work, hereby publish it under the following license:
Creative Commons CC-Zero This file is made available under the Creative Commons CC0 1.0 Universal Public Domain Dedication.
The person who associated a work with this deed has dedicated the work to the public domain by waiving all of their rights to the work worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law. You can copy, modify, distribute and perform the work, even for commercial purposes, all without asking permission.

GIF development
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N
 
This GIF graphic was created with GNU Octave.
Octave/gnuplot source
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click to expand

This graphic was created by the following Octave script:

graphics_toolkit gnuplot

  N = 256;                % sams_per_fft;
  window = blackmanharris(N)/sum(blackmanharris(N));
  A = -N/2;               % left  limit of plots
  B=  N/2-1;              % right limit of plots
%
  Fs = N;                 % sams_per_sec;
  HzPerBin = Fs/N;
  freq_bin = 9+1/sqrt(2); % any signal frequency not harmonically related to Fs
  freq_Hz = freq_bin*HzPerBin;
%
  L = 120000;                   % amount of data to average
  n = 1:L;
  x = exp(j*2*pi*freq_Hz/Fs*n); % non-quantized signal
  sig8 = round(2^8 * x)/2^8;
  sig6 = round(2^6 * x)/2^6;
%
  sams_per_offset = 0.75*N;     % overlap = 25%
%
% number of samples available beyond just one FFT
  excess_sams = length(x) - N;
%
  j1 = floor( excess_sams / sams_per_offset );
  sams_per_offset = floor( excess_sams / j1 );
  num_ffts = 1 + j1;
%
% define the first block of data
  samples = 1:N;
%
  amplitude8 = zeros(1,N);
  amplitude6 = zeros(1,N);
%
% Loop over all the available blocks
  for j1 = 1 : num_ffts
    amplitude8 = amplitude8 + abs(fft( sig8(samples) .* window ));
    amplitude6 = amplitude6 + abs(fft( sig6(samples) .* window ));
    samples = samples + sams_per_offset;
  end
%
  amplitude8  = 20*log10(fftshift(amplitude8/num_ffts));
  amplitude6  = 20*log10(fftshift(amplitude6/num_ffts));
%
  abscissa = A:B;
  figure (1, 'color', .95*[1 1 1])
  subplot(2,1,1);
  h = area(abscissa, amplitude6(abscissa +N/2+1), ...
  'FaceColor', [.871 .49 0], 'edgecolor', [.871 .49 0]);
  set(h,'BaseValue',-90)
  set(gca, 'YTick', [0 -40 -68 -90])
  set(gca, 'XTick', [])
  set(gca, 'YGrid','on', 'color', 'white')
  xlim([A B])
  ylim([-90 2])
  text(A, 10, '6 bits')
  xlabel('\leftarrow  frequency  \rightarrow', 'fontsize', 10)
  ylabel('decibels', 'fontsize', 10)
  title('Spectral view of a sinusoid and its quantization noise-floor','fontsize', 12);
% Move subplot downward to prevent title being cropped by gnuplot bug.
  set(gca, "position", get(gca, "position") - [0 0 0 0.02])  
%
  subplot(2,1,2);
  h = area(abscissa, amplitude8(abscissa +N/2+1), ...
  'FaceColor', [.871 .49 0], 'edgecolor', [.871 .49 0]);
  set(h,'BaseValue',-90)
  set(gca, 'YTick', [0 -40 -80])
  set(gca, 'XTick', [])
  set(gca, 'YGrid','on', 'color', 'white')
  xlim([A B])
  ylim([-90 2])
  text(A, 10, '8 bits')
  xlabel('\leftarrow  frequency  \rightarrow')
  ylabel('decibels', 'fontsize', 10)

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4 April 2014

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Date/TimeThumbnailDimensionsUserComment
current14:29, 4 April 2014Thumbnail for version as of 14:29, 4 April 2014864 × 438 (11 KB)Bob KUser created page with UploadWizard

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