第05章 离散时&eacut

第05章 离散时&eacut

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5.5 all-pass system (全通系统) |( ) | c o n s t a n t j ap He ω = An all-pass system is defined as a system for which the frequency-response magnitude is a constant 1* * 1 ** * () 1 / , 1 1( 1 ) ) | 1 11 1 j jj j j j za Hz a a r e az ea a e a e e e ae θ ωω −− == = = ,零点: 极点 EXAMPLE - (1 ) sin( ) arg[ ( )] arg{ } 2arctan{ } c o s ( ) j j ap er e e r re e r ωθ θω
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= = = c r M k k k k k M k k k ap z e e z z e e z z d d z A z H 1 1 * 1 1 * 1 1 1 1 ) 1 ( ) ( ) 1 ( ) ( 1 ) ( The most general form for the system function of an all-pass system with a real-valued impulse response is Where A is a positive constant and the d k ’s are real, and the e k ’s are complex. Characters of poles and zeros: complex zeros and poles being paired with their conjugates. 零点和极点共轭反演 ; 若实系数,零点对互为共轭,极点对 互为共轭。
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4/3 3/4 EXAMPLE Y Y Y N Determine whether or not each system is an all-pass system . z= ∞有零点 无穷远有零点
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0 )] ( [ > ω j ap e H grd π < < < 0 , 0 )] ( arg[ for e H j ap () ' , | ( ) || ' ( ) | jj ap Hz H z H z He H e ωω == 用途: 1. 补偿相位失真 2. 与最小相位系统合作补偿幅度失真 ) ( ) ( ). ( min z H z H z H ap = 证明见教材 有相位失真 补偿相位失真 无相位失真 有幅度失真 补偿幅度失真 无幅度失真 5.5 节总结:全通系统无幅度失真,零点和极点共轭反演。 Properties of causal stable all-pass system
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5.5 节 思考题 设因果 LTI 系统的差分方程是
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