File:Scalloping and noise floor comparisons (2 window functions).png

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Scalloping_and_noise_floor_comparisons_(2_window_functions).png (562 × 457 pixels, file size: 22 KB, MIME type: image/png)

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English: Comparison of two window functions in terms of their effects on equal-strength sinusoids with additive noise. The noise "floor" is smoothed by averaging many DFTs to reveal the substantial difference in levels, caused by the different window functions. The sinusoid at bin -20 suffers no scalloping and the one at bin +20.5 exhibits worst-case scalloping. The rectangular window produces the most scalloping but also narrower peaks and lower noise-floor. A third sinusoid with amplitude -16 dB would be noticeable in the upper spectrum, but not in the lower spectrum.
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Author Bob K
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Matlab code

N = 256;                % sams_per_fft;
  window1 = rectwin(N)'/sum(rectwin(N));
  window2 = blackmanharris(N)'/sum(blackmanharris(N));
%
  Fs = N;                 % sams_per_sec;
  HzPerBin = Fs/N;
  F1 = -20.0*HzPerBin;    % bin -20
  F2 = +20.5*HzPerBin;    % bin 20.5
%
  L = 100000;
  n = 1:L;
  x = exp(j*2*pi*F1/Fs*n) + exp(j*2*pi*F2/Fs*n);
  x = x + (randn(1,L) +j*randn(1,L))*1.4;
%
  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;
%
  amplitude1 = zeros(1,N);
  amplitude2 = zeros(1,N);
%
% Loop over all the available blocks
  for j1 = 1 : num_ffts
    amplitude1 = amplitude1 + abs(fft( x(samples) .* window1 ));
    amplitude2 = amplitude2 + abs(fft( x(samples) .* window2 ));
    samples = samples + sams_per_offset;
  end
%
  warning off MATLAB:log:logOfZero
  amplitude1  = 20*log10(fftshift(amplitude1/num_ffts));
  amplitude2  = 20*log10(fftshift(amplitude2/num_ffts));
% 
  abscissa = -40:40;
  figure
  subplot(2,1,1); h = area(abscissa, amplitude1(abscissa +N/2+1), ...
  'FaceColor', [.871 .49 0], 'Linestyle', 'none')
  set(h,'BaseValue',-20)
  xlim([-40 40])
  ylim([-20 2])
  set(gca,'XTick', [-20 0 20.5])
  set(gca,'YGrid','on')
  xlabel('DFT bins')
  ylabel('decibels')
  title('Rectangular windowing');
%
  subplot(2,1,2); h = area(abscissa, amplitude2(abscissa +N/2+1), ...
  'FaceColor', [.871 .49 0], 'Linestyle', 'none')
  set(h,'BaseValue',-20)
  xlim([-40 40])
  ylim([-20 2])
  set(gca,'XTick', [-20 0 20.5])
  set(gca,'YGrid','on')
  xlabel('DFT bins')
  ylabel('decibels')
  title('Blackman-Harris windowing');

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Date/TimeThumbnailDimensionsUserComment
current17:46, 19 December 2011Thumbnail for version as of 17:46, 19 December 2011562 × 457 (22 KB)Bob K (talk | contribs)Change graph format to area fill to highlight noise floor comparison.
16:52, 19 December 2011Thumbnail for version as of 16:52, 19 December 2011572 × 461 (24 KB)Bob K (talk | contribs)

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