Quantization noise demo

README

Show the effect of ADC/DAC quantization noise.

quant.m

% To show the effect of quantization noise, we take a signal and quantize
% it (by rounding to the nearest integer).   Taking the difference gives
% the quantization error.  We then display the amplitude spectra of all
% three signals (original, quantized, and error).  Finally, we compare to
% the theoretically expected quantization noise spectral density of
% 1/sqrt(6*fs) (valid with some assumptions; i.e. all quantization levels
% uniformly visited?).

% Tobin Fricke 2012-01-06

fs = 1024;                    % sample rate [Hz]

t = 0:(1/fs):16;              % time vector [s]

% make a sinusoid
%A = 32768;                    % amplitude in quantization levels
%f = 20*exp(1)/3;
%x = A*sin(2*pi*f*t);          % original signal

% make random noise
x = 4*randn(size(t));                   % white noise
[B,A] = ellip(4, 3, 100, [10 200]/(fs/2),'stop');
%[B,A] = butter(4, 10/(fs/2), 'low');
x = filter(B, A, x);
y = round(x);                 % quantized signal
n = y - x;                    % quantization error (noise)

%plot(t, x, t, y, t, n);

bw = 0.5;                     % spectrum resolution (Hz)
nfft = fs/bw;                 % length of fft (samples)

[Pxx, f] = pwelch(x, hanning(nfft), nfft/2, nfft, fs);
[Pyy, f] = pwelch(y, hanning(nfft), nfft/2, nfft, fs);
[Pnn, f] = pwelch(n, hanning(nfft), nfft/2, nfft, fs);

loglog(f, sqrt(Pxx), f, sqrt(Pyy), f, sqrt(Pnn));

LSBvoltage = 1;
quant_noise_pred = LSBvoltage / sqrt(6*fs);

line(get(gca,'xlim'), quant_noise_pred*[1 1], 'color', [0 0 0], 'linestyle', '--');
grid on
xlim([bw (fs/2)])

legend('signal', 'signal (quantized)', 'quant. error', 'expected quant noise', ...
  'Location', 'Best');

xlabel('frequency');
ylabel('counts per sqrt Hz');
title('quantization noise - amplitude spectral density');

quant_demo.pdf