第05章 离散时&eacut

第05章 离散时&eacut

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5.7 linear system with generalized linear phase system 5.7.1 definition 5.7.2 conditions of generalized linear phase system 5.7.3 causal generalized linear phase (FIR)system
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5.7.1 definition linear-phase system (线性相位系统) () | | | | arg[ ( )] ( ) [( ) ] ( ) jj j j j He e H e line grd H e real ωω ω α π ωα = < =− = δ < = = = = | | ) ( ] [ ] [ ] [ ] [ ] [ ] [ m j j id id id e e H m n x n h n x n y m n n h EXAMPLE Ideal delay system : A linear-phase system
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h=[0 0 0 0 0 0 1 0 0 0 0 0 0]; [H,f]=freqz(h,1); figure; plot(f, phase( (H))) figure; plot(f, angle( (H))) figure; grpdelay(h,1) 连续相位 主值相位 设理想延迟系统的 m=6 群延迟 h[n]=delta[n-6]
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() || arg[ ( )] , [( ) ] jj j j j j j He Ae e A e is a real function grd H e ωω ω α β π ωα β −+ = < =− + = /2 / , 0 , / 2 , , 0 , 0 j j j j T e Ae TT e T e T ωπ ωα πω = == = = << = −≤ < EXAMPLE Differentiator: A generalized linear-phase system generalized linear-phase system (广义线性相位系统)
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These two kind of system can all be characterized by constant group delay (常数群延迟系统) . /2 ,0 1,0 () 0 1, 0 2 /2,0 , | | 1 , a r g { } /2, 0 j jj j j j j je He Ae e e π ωω ω ωπ αβ πω ππ −= < < < < = == = ⎨⎨ −≤ < =− < << = ≤< < ,, EXAMPLE Hilbert transform: A generalized linear-phase system
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EXAMPLE Causal moving average system : A generalized linear-phase system 4 0 2 1 [] [ ] 5 1sin( 5/2) () 5s in ( /2 ) k j j hn n k He e ω δ = =− = h=[1 1 1 1 1]/5; [H,f]=freqz(h,1); figure; plot(f,abs(H)); figure; plot(f, phase((H))) 严格幅度 连续相位: 幅度过零点时相位突变 PI 广义 连续相位是直线。 严格相位
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原方波信号 线性相位低通滤波后信号 非线性相位滤波后信号 EXAMPLE 线性相位和非线性相位低通 系统对信号波形的影响
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广义线性相位系统级联仍然广义线性相位; 并联则不一定,条件是参数相同。 5.7.1 小结 线性相位及广义线性相位的定义; 对所有通带内频率延迟相同采样点,频率高的相位延迟大; 线性相位的优点。 11 2 2 12 1 2 () ()() jj j j j j j He H e H e A e e A e e Ae A e e ω αβ α β ωω ωα α β β −+ + + + == = 1 2 j j jjj j j H e H e A e e A e e A e e ωωω ωα =+ = + ⎡⎤ ⎣⎦ 广义线性相位系统的级联和并联
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5.7.2 (sufficient ) conditions of generalized linear phase system 0/ 2 3 / 2 (1) 2 (integer) (2) 2 [2 ] [ ] ] or MM hn h n h n β πβ π αα == ⎧⎧ ⎪⎪ ⎨⎨ −= ⎩⎩
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This note was uploaded on 02/29/2012 for the course EE 325 taught by Professor Lilili during the Fall '11 term at BYU.

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