Add experiment

1 - experiment/Circulant Matrix/circulant_matrix.m

@@ -0,0 +1,47 @@
+%%
+clc;
+clear;
+
+N = 100;
+eps = 1e-10;
+F_n = dftmtx(N);
+
+for i = 1: N
+    for j = 1: N
+        fprintf(string(F_n(i, j)) + ", ");
+    end
+    fprintf("\b\b\n");
+end
+
+fprintf("\n");
+
+% 检查傅里叶矩阵的正确性
+assert(abs(F_n(2, 2) ^ 2 - F_n(2, 3)) < eps);
+assert(abs(F_n(2, 2) ^ N - 1) < eps);
+
+%% 检查循环卷积
+x = randn(N, 1);
+z = randn(N, 1);
+p = cconv(x, z, N);
+
+% 检查循环卷积公式的正确性
+for i = 1: N
+    tmp = 0;
+    for j = 1: N
+        tmp = tmp + x(j) * z(mod(i-j+N, N)+1);
+    end
+    assert(abs(tmp - p(i)) < eps);
+end
+
+% 检查 x * z = A(x)z 的正确性
+A_x = toeplitz([x(1) fliplr(x(2:end)')], x);
+assert(is_vector_equal(p, A_x' * z, eps));
+
+% 检查卷积定理的正确性
+x_hat = fft(x);
+z_hat = fft(z);
+xz_hat = fft(p);
+assert(is_vector_equal(x_hat .* z_hat, xz_hat, eps));
+
+
+

1 - experiment/Circulant Matrix/is_vector_equal.m

@@ -0,0 +1,5 @@
+function flg = is_vector_equal(A, B, eps)   
+    diff = abs(A - B);
+    max_diff = max(diff);
+    flg = max_diff <= eps;
+end