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