IIR濾波器設(shè)計總結(jié)1

IIR模擬濾波器設(shè)計1.低通Butterworth濾波器設(shè)計(1)技術(shù)指標(biāo)通帶截止頻率：阻帶截止頻率：通帶最大衰減：阻帶最小衰減：3dB截止頻率：(2)歸一化，，(3)濾波器階數(shù)，，（向上取整）(4)濾波器3dB截止頻率，阻帶有余量，，通帶有余量(5)極點極點：歸一化極點：(6)系統(tǒng)函數(shù)：，歸一化系統(tǒng)函數(shù)：2.低通ChebyshevI型濾波器設(shè)計(1)技術(shù)指標(biāo)通帶截止頻率：阻帶截止頻率：通帶最大衰減：阻帶最小衰減：3dB截止頻率：(2)歸一化，(3)濾波器階數(shù)，，（向上取整）(4)極點極點實部：，極點虛部：，歸一化極點：(5)系統(tǒng)函數(shù)系統(tǒng)函數(shù)：，歸一化系統(tǒng)函數(shù)：2.頻率變換模擬低通濾波器的頻率變換：歸一化原型低通濾波器截止頻率為1，則有類型映射新截止頻率低通高通帶通：上限截止頻率：下限截止頻率帶阻：上限截止頻率：下限截止頻率3.IIR數(shù)字濾波器設(shè)計(1)脈沖響應(yīng)不變法(a)DF指標(biāo)AF指標(biāo)(b)將得到的模擬域指標(biāo)映射為對應(yīng)的歸一化低通指標(biāo)類型指標(biāo)歸一化映射歸一化低通濾波器參數(shù)高通，，，，，帶通，，，，，，，，，，，帶阻，，，，，，，，，，，(c)設(shè)計歸一化低通butterworth模擬濾波器(chebyshev濾波器)(d)映射為所需類型的歸一化AF(d)去歸一化，得到要設(shè)計的AF(e)將AF傳遞函數(shù)分解為一階部分分式之和：(f)將上式中每個部分分式映射為Z域表示：。(2)雙線性變換法(a)DF指標(biāo)AF指標(biāo)(b)將得到的模擬域指標(biāo)映射為對應(yīng)的歸一化低通指標(biāo)（見上頁表格）(c)設(shè)計歸一化低通butterworth模擬濾波器(chebyshev濾波器)(d)映射為所需類型的歸一化AF(d)去歸一化，得到要設(shè)計的AF(e)將AF傳遞函數(shù)映射為待設(shè)計的DF：*對chebyshev濾波器，高通和低通歸一化時不用3dB截止頻率而用通帶截止頻率。4.低通數(shù)字濾波器的Z域直接頻率變換原型數(shù)字濾波器3dB截止頻率為，則有類型映射設(shè)計參數(shù)低通：目的濾波器截止頻率高通：目的濾波器截止頻率帶通：帶通DF通帶下限截止頻率：帶通DF通帶上限截止頻率帶阻：帶通DF通帶下限截止頻率：帶通DF通帶上限截止頻率濾波器結(jié)構(gòu)變換residuezz-transformpartial-fractionexpansionsos2tfConvertdigitalfiltersecond-ordersectiondatatotransferfunctionformsos2zpConvertdigitalfiltersecond-ordersectionparameterstozero-pole-gainformtf2sosConvertdigitalfiltertransferfunctiondatatosecond-ordersectionsformtf2zpConverttransferfunctionfilterparameterstozero-pole-gainformtf2zpkConverttransferfunctionfilterparameterstozero-pole-gainformzp2sosConvertzero-pole-gainfilterparameterstosecond-ordersectionsformzp2tfConvertzero-pole-gainfilterparameterstotransferfunctionform模擬濾波器設(shè)計Butterworth低通濾波器[z,p,k]

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butter(n,Wn,'s')

[z,p,k]

=

butter(n,Wn,'ftype','s')

[b,a]

=

butter(n,Wn,'s')

[b,a]

=

butter(n,Wn,'ftype','s')

直接設(shè)計數(shù)字濾波器[z,p,k]

=

butter(n,Wn)

[z,p,k]

=

butter(n,Wn,'ftype')

[b,a]

=

butter(n,Wn)

[b,a]

=

butter(n,Wn,'ftype')ChebyshevI型低通濾波器設(shè)計

[z,p,k]

=

cheby1(n,R,Wp,'s')

[z,p,k]

=

cheby1(n,R,Wp,'ftype','s')

[b,a]

=

cheby1(n,R,Wp,'s')

[b,a]

=

cheby1(n,R,Wp,'ftype','s')[z,p,k]

=

cheby1(n,R,Wp)

[z,p,k]

=

cheby1(n,R,Wp,'ftype')

[b,a]

=

cheby1(n,R,Wp)

[b,a]

=

cheby1(n,R,Wp,'ftype')

濾波器頻帶變換FrequencyTransformationTransformationFunctionLowpasstolowpass[numt,dent]

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lp2lp(num,den,Wo)[At,Bt,Ct,Dt]

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lp2lp(A,B,C,D,Wo)Lowpasstohighpass[numt,dent]

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lp2hp(num,den,Wo)[At,Bt,Ct,Dt]

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lp2hp(A,B,C,D,Wo)Lowpasstobandpass[numt,dent]

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lp2bp(num,den,Wo,