離散系統(tǒng)的系統(tǒng)函數(shù)和頻率響應.ppt
離散系統(tǒng)的系統(tǒng)函數(shù)和頻率響應,系統(tǒng)函數(shù):,頻率響應: 單位圓上的系統(tǒng)函數(shù)(傳輸函數(shù)),穩(wěn)定性:,(穩(wěn)定的系統(tǒng)收斂域包括單位圓),1、零極點分布對系統(tǒng)因果、穩(wěn)定性的影響:,離散系統(tǒng)穩(wěn)定的充分必要條件是: The ROC of H(z) contain the unit circle(單位圓),unit circle,unit circle,unit circle,Causality ( 因果性 ):,in the z-domain,因果、穩(wěn)定系統(tǒng):,2、利用零極點分布確定系統(tǒng)的頻率特性:,位于原點的零極點不影響 只影響,設系統(tǒng)穩(wěn)定,將z=ejw代入上式,相量相減的矢量幾何表示法:從Cr單位圓上的ejw,零點矢量,極點矢量,B為單位圓上的一點,對應jw的角度,Cr是零點,dr是極點,單位圓附近的零點,使得,分子變小,形成波谷,越靠近單位圓,波谷 越低,極點使 形成波峰,極點越靠近 單位圓,波峰越尖銳。,例1:The shape of the spectrum X( ) is affected by the pole/zero pattern of the z-transform X(z).,2.6 Transfer functions,Equivalent Descriptions of Digital Filters system function H(z)(傳遞函數(shù)) Frequency response/transfer function H( )(頻率響應) Block diagram realization and sample processing algorithm(方框圖及采樣算法描述) I/O difference equation (輸入輸出差分方程) Pole/zero pattern(零極點描述) Impulse response h(n)(沖激響應) I/O convolutional equation(卷積),system function,H(z),impulse response,h(n),I/O convolutional,equation,pole/zero,pattern,I/O difference,equation(s),filter design,method,frequency response Transfer function,H( ),block-diagram,realization,sample,processing,filter design,specifications,2.7 Pole/Zero Designs,設某一離散因果穩(wěn)定系統(tǒng)有一對共軛復數(shù)極點。,0<R<1,We obtain the transfer function:,Where a1=-2Rcos 0, a2=R.,If |H(0)|=1, then,Resonator-諧振器,3-dB width-3 分貝帶寬,1/2,1,0,0,/2, Notch and Comb Filters,|H()|,0,陷波器,梳狀濾波器,pole,zero,