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109年 - 109 國立中山大學_碩士班招生考試_資工系(乙組):工程數學#105759
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題組內容
I Discrete Fourier Transform (DFT) is a widely used transformation method in signal processing. According to DFT matrix, please determine the correctness of the following descriptions.
3. DFT matrix is an unitary matrix.
其他申論題
(b) If the graph has 72 edges, what is m?
#450110
9. For a, b,n ∈ Z⁺ and n > 1, prove that a ≡ b (mod n) gcd(a,n) = gcd(b,n).
#450111
1.All circulant matrices are made diagonal by the Discrete Fourier Transform (DFT), regardless of the generating vector x.
#450112
2..DFT matrix is not a kind of symmetric matrix.
#450113
4.The DFT is a linear transform.
#450115
5. The orthogonality is not the property of the DFT matrix.
#450116
6. The determinant of A is 6.
#450117
7. The trace of A is 7.
#450118
8. The rank(A-1)=3, where I is the 4x4 identity matrix.
#450119
9. The determinant of the adjoint matrix At is 6.
#450120