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

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
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(Reusing this file)
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Category:CC-Zero#Frequency%20spectrum%20of%20a%20sinusoid%20and%20its%20quantization%20noise%20floor.gif
Category:Self-published work
GIF development
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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)
Category:Digital signal processing Category:English text Category:Quantization Category:Created with GNU Octave Category:Images with Octave source code Category:Images with Gnuplot source code
Category:CC-Zero Category:Created with GNU Octave Category:Digital signal processing Category:English text Category:Images with Gnuplot source code Category:Images with Octave source code Category:PNG created with Octave Category:Pages using deprecated source tags Category:Quantization Category:Self-published work