Add example

2024-05-09 16:54:58 +08:00
parent b91a609ca5
commit 17386d80c1
24 changed files with 3344 additions and 1 deletions
@@ -0,0 +1,52 @@
+clc; clear;
+
+phi = 0.5 * pi;
+N = 5000;
+t = linspace(-2 * pi, 2 * pi, N)';
+x = sin(2 * pi * t) + 3 * sin(3 * 2 * pi * t);
+x_2 = sin(2 * pi * t + phi) + 3 * sin(3 * 2 * pi * t + phi);
+
+f = fftshift(fft(x));
+F = dftmtx(N);
+f_hat = fftshift(F * x);
+
+f_2 = fftshift(fft(x_2));
+
+J = circshift(eye(N), 1, 2);
+[J_eigenvector, J_eigenvalue] = eig(J);
+J_eigenvalue = diag(J_eigenvalue);
+
+CMatrix = toeplitz(x);
+[CMatrix_eigenvector, CMatrix_eigenvalue] = eig(CMatrix);
+CMatrix_eigenvalue = diag(CMatrix_eigenvalue);
+
+CMatrix_eigenvalue_hat = zeros(size(CMatrix_eigenvalue));
+for i = 1: N
+    tmp = f(i) * J_eigenvalue(i) ^ (i - 1);
+    CMatrix_eigenvalue_hat(i) = CMatrix_eigenvalue_hat(i) + tmp;
+end
+
+
+if 1 == 1
+    subplot(311);
+    plot(x);
+    
+    subplot(312);
+    plot(abs(f));
+    
+    subplot(313);
+    % plot(abs(f_hat));
+    plot(abs(f_2));
+
+    % polarplot(angle(J_eigenvalue),abs(J_eigenvalue),"o")
+else
+    subplot(311);
+    plot(abs(f_hat));
+    
+    subplot(312);
+    plot(sort(abs(CMatrix_eigenvalue)));
+
+    subplot(313);
+    plot(sort(abs(CMatrix_eigenvalue_hat)));
+    
+end