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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.
4.The DFT is a linear transform.
其他申論題
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
3. DFT matrix is an unitary matrix.
#450114
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
10. The matrix A is a simple matrix.
#450121