This graphics has been realized with the help of the following Octave script:

#-------------------------------------------------------------------------------
# Specifications
#
bitNb = 8;
clockFrequency = 100E6;
outputFrequency = clockFrequency / (2^(bitNb-4));
outputFrequency = 7/8 * outputFrequency;
fftMin = -100;
printFigures = 1;

pointNb = 2^bitNb;

#===============================================================================
# DDS time signals
#
step = round(2^bitNb * (outputFrequency/clockFrequency));
sawtooth = zeros(1, pointNb);
for index = 2:length(sawtooth)
  sawtooth(index) = rem(sawtooth(index-1) + step, 2^bitNb);
endfor
msb = sawtooth >= 2^(bitNb-1);
sine = sin(sawtooth*(2*pi)/2^bitNb);

figure(1);
time = [1:length(sawtooth)] / clockFrequency;
plot(time, sawtooth, 'g');
hold on;
plot(time, msb*2^(bitNb-1), 'r');
plot(time, sine*2^(bitNb-2)+2^(bitNb-2), 'b');
hold off;
xlabel('time');
ylabel('DDS outputs');
title(['Direct Digital Synthesizer, ', ...
  sprintf('%d', bitNb), ' bits, step = ', ...
  sprintf('%d', step)]);
grid;
if (printFigures != 0)
  print -dsvg dds_time.svg
endif

#-------------------------------------------------------------------------------
# Fourier transform
#
msbTransform = 20*log10(abs(fft(2*(msb-0.5)))/length(msb));
msbTransform(msbTransform < fftMin) = fftMin;
sineTransform = 20*log10(abs(fft(sine))/length(msb));
sineTransform(sineTransform < fftMin) = fftMin;
frequency = linspace(0, clockFrequency, pointNb);

figure(2);
plot(frequency, msbTransform, 'r');
hold on;
plot(frequency, sineTransform, 'b');
hold off;
xlabel('frequency');
ylabel('DDS outputs FFT');
title(['Direct Digital Synthesizer, ', ...
  sprintf('%d', bitNb), ' bits, step = ', ...
  sprintf('%d', step)]);
grid;
if (printFigures != 0)
  print -dsvg dds_frequency.svg
endif

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