English: Spectrum of a 750 Hz pure tone sampled at 48 kHz and quantized to 4 bits using triangular dither but no noise shaping.

% quantization_dither_noshaping.m
% Quantization demo using dither but no noise shaping.
% Authors: Fatbag
% License: Public domain (no warranties)

rand('state', 0xdeadbeef);

f_s = 48000; % sampling rate (samples/sec)
f0 = 750; % frequency of sine wave (Hz)

t_s = 1/f_s; % sampling period (sec/sample)
w0 = 2*pi*f0; % angular frequency of sine wave (Hz)

t = (0 : 4095) * t_s;

x = round(15*sin(w0*t) + rand(1, length(t)) - 0.5 + rand(1, length(t)) - 0.5);

figure 1;
plot(t(1:ceil(2*f_s/f0)), x(1:ceil(2*f_s/f0)));
axis([0, ceil(2*f_s/f0)*t_s, -20, 20]);
grid on;
xlabel('t');
ylabel('x(t)');

figure 2;
X = fft(x(1:4096));
X = X(1:2048);
m = 20*log10(arrayfun(@norm, X));
m -= max(m);
m(~isfinite(m)) = -1000;
f = (0:2047)/2048*f_s/2;
plot(f, m);
axis([0, f_s/2, -100, 0]);
grid on;
xlabel('Frequency (Hz)');
ylabel('Relative power (dB)');
print 'quantization_dither_noshaping_spectrum_uncropped.png';