%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% exmp2_11.m - Waveform and spectrum of sinewave corrupted by
%              white noise with Signal-to-noise ratio = 10 dB
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

N=256; A=sqrt(20); w0=0.2*pi;  % define parameters
n = [0:N-1];                   % time index
sn = A*sin(w0*n);              % sine sequence
vn = (rand(1,N)-0.5)*sqrt(12); % zero-mean, unit-variance white noise
xn = sn+vn;                    % sinewave embedded in white noise
subplot(2,1,1);                % top figure
plot(n,xn)                     % plot the waveform
title('Waveform of noisy sinewave');
xlabel('Time index n'); ylabel('Amplitude');
axis([0 255 -inf inf])
Xk = fft(xn);                  % compute DFT
absXk = 20*log10(abs(Xk));     % magnitude spectrum in dB
subplot(2,1,2);                % bottom figure
plot(n,absXk)                  % plot the spectrum
title('Spectrum of noisy sinewave');
xlabel('Frequency index k'); ylabel('Magnitude in dB');
axis([0 127 -inf inf])