| ชื่อเรื่อง | : | Eigenvalues and equivalent transformation of a trigonometric matrix associated with filter design. |
| นักวิจัย | : | Liu, Yiying. , Lin, Zhiping. , Molteni, Giuseppe. , Zhang, Dongye. |
| คำค้น | : | DRNTU::Engineering::Electrical and electronic engineering. |
| หน่วยงาน | : | Nanyang Technological University, Singapore |
| ผู้ร่วมงาน | : | - |
| ปีพิมพ์ | : | 2555 |
| อ้างอิง | : | Liu, Y., Lin, Z., Molteni, G., & Zhang, D. (2012). Eigenvalues and equivalent transformation of a trigonometric matrix associated with filter design. Linear algebra and its applications, 437(12), 2961-2972. , http://hdl.handle.net/10220/17655 , http://dx.doi.org/10.1016/j.laa.2012.06.031 |
| ที่มา | : | - |
| ความเชี่ยวชาญ | : | - |
| ความสัมพันธ์ | : | Linear algebra and its applications |
| ขอบเขตของเนื้อหา | : | - |
| บทคัดย่อ/คำอธิบาย | : | The N × N trigonometric matrix P(ω) whose entries are P(ω)(i, j) =1/2 (i+j−2) cos(i−j)ω appears in connection with the design of finite impulse response (FIR) digital filters with real coefficients. We prove several results about its eigenvalues; in particular, assuming N⩾4 we prove that P(ω) has one positive and one negative eigenvalue when ω/π is an integer, while it has two positive and two negative eigenvalues when ω/π is not an integer. We also show that for ω/π not being an integer and a sufficiently large N, the two positive eigenvalues converge to α+N2 and the two negative eigenvalues to α-N2, where α± = (1 ± 2/√3)/8. Furthermore, an equivalent transformation diagonalizing P(ω) is described. |
| บรรณานุกรม | : |
Liu, Yiying. , Lin, Zhiping. , Molteni, Giuseppe. , Zhang, Dongye. . (2555). Eigenvalues and equivalent transformation of a trigonometric matrix associated with filter design..
กรุงเทพมหานคร : Nanyang Technological University, Singapore. Liu, Yiying. , Lin, Zhiping. , Molteni, Giuseppe. , Zhang, Dongye. . 2555. "Eigenvalues and equivalent transformation of a trigonometric matrix associated with filter design.".
กรุงเทพมหานคร : Nanyang Technological University, Singapore. Liu, Yiying. , Lin, Zhiping. , Molteni, Giuseppe. , Zhang, Dongye. . "Eigenvalues and equivalent transformation of a trigonometric matrix associated with filter design.."
กรุงเทพมหานคร : Nanyang Technological University, Singapore, 2555. Print. Liu, Yiying. , Lin, Zhiping. , Molteni, Giuseppe. , Zhang, Dongye. . Eigenvalues and equivalent transformation of a trigonometric matrix associated with filter design.. กรุงเทพมหานคร : Nanyang Technological University, Singapore; 2555.
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