fg_03_13.m

英文书《Digital Signal Processing with Examples in MATLAB》附带的MATLAB实例

% page_63 Two reconstructions, one w/ aliasing.
% Fourier series coefficients for x(t).
M=10;  m=1:M-1; t=linspace(0,10,500);
b=1./(m.^.5);
ax=[0 10 -3.5 3.5];

% Continuous plot of x(t).
N=500; n=0:N-1; T=10/N;
x=b*sin(2*pi*m'*n/N);
sp_fig(1);
subplot(3,1,1);
axis(ax);
set(gca,'fontsize',16);
line(t,x,'color','k'); grid;
ylabel('Original {x}({t})');
h=text(4.1,2.7,'Frequency range of {x}({t}) = [0,1) Hz.');
set(h,'fontsize',16);

% Reconstruction w/o aliasing.
N=20; n=0:N-1; T=10/N;
xn=b*sin(2*pi*m'*n/N);
subplot(3,1,2);
axis(ax);
set(gca,'fontsize',16);
line(n*T,xn,'color','k','linestyle','none','marker','o');
X=fft(xn);
omg_0=2*pi/T;
m2=1:fix((N-1)/2);
x1=(1/N)*(X(1)+2*real(X(2:fix((N+1)/2))*exp(j*omg_0*m2'*t/N)));
line(t,x1,'linestyle','-','color','k'); grid;
ylabel('Reconstruct.');
h=text(4.1,2.7,'Sampling rate = 2 samples/s');
set(h,'fontsize',16);

% Reconstruction w/ aliasing.
N=15; n=0:N-1; T=10/N;
xn=b*sin(2*pi*m'*n/N);
subplot(3,1,3);
axis(ax);
set(gca,'fontsize',16);
line(n*T,xn,'color','k','linestyle','none','marker','o');
X=fft(xn);
omg_0=2*pi/T;
m2=1:(N-1)/2;
x2=(1/N)*(X(1)+2*real(X(2:(N+1)/2)*exp(j*omg_0*m2'*t/N)));
line(t,x2,'linestyle','-','color','k'); grid;
line(t,x,'linestyle','--','color','k');
xlabel('{t} (s)'); ylabel('Reconstruct.');
h=text(4.1,2.7,'Sampling rate = 1.5 samples/s');
set(h,'fontsize',16);