Passive, active, and digital filters (3ed., CRC, 2009) - tiera.ru

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Low-Gain Active Filters 11-23TABLE 11.1Properties of Sensitivity FunctionS kyx ¼ S y kx ¼ Sy x S y1=y2x ¼ S y1xS x x ¼ Skx x¼ S kxkx ¼ 1 Sy x1¼ S y x2S y2x1S y 1=x ¼ S1=y x ¼ S y x S y x ¼ S jyjxS y1y2xQ ni¼1 yix ¼ Pni¼1S¼ S y1x þ S y2xS yixS y2xþ j arg yS arg yxS arg yx ¼ 1arg y Im Sy x(*)S jyjxS ynx ¼ nS y x S yþxS xnx¼ S kxnx¼ n¼ Re S y x(*)x ¼ 1yþzP ni¼1 yix ¼S y x n ¼ 1 n Sy x S 1n yx ¼ 11n y Sy xS x x n ¼ Sx kx n ¼ 1 nSyS y x þ zS z xP ni¼1 yiSy iP ni¼1 yi xSource: Huelsman, L.P. and Allen, P.E., Introductionto the Theory and Design of Active Filters, McGraw-Hill,New York, 1980.Note: Relations denoted by ‘‘(*)’’ use y to indicate acomplex quantity and x to indicate a real quantity.Not that the quantity Dv o =v o represents a small differential change in the cutoff frequency v o . Whenconsidering the root locus of a filter design, the change in pole location due to a change in gain K, forexample, could be described by [3]S p 1K ¼ @s oþ j @v o K@K @Kv o(11:75)where the pole p 1 ¼ s o þ jv o . Furthermore, the filter transfer function’s magnitude and phase sensitivityis defined by [3]andT( jv)Sx¼ Sj T( jv)xju( jv)þ SxT( jv)¼ Re Sx þ 1 jv)Im ST(x(11:76)u(v)x ¼ x @T( jv)jT( jv) j @x j @u(v)jþjx@xT( jv)S(11:77)where T(jv) ¼jT(jv)jexp[ju(v)]. The interested reader is directed to Ref. [5, Chapter 3] for a detaileddiscussion of sensitivity.11.7.2 Gain-BandwidthNow let us consider some of the amplifier nonidealities that influence the performance of our low-gainamplifier filter realizations. There are two amplifier implementations of interest each using an operationalamplifier. They are the noninverting configuration and the inverting configuration shown in Figure 11.21.The noninverting amplifier is described byK ¼ V 2 A d (s)¼(11:78)V 1 1 þ A d (s)=K o
11-24 Passive, Active, and Digital Filters++–+V 1 V 2R BR A––R AR B++–V 1 +V 2––(a)(b)FIGURE 11.21(a) Noninverting amplifier and (b) inverting amplifier.whereK o ¼ 1 þ R B =R A is the ideal gainA d (s) is the operational amplifier’s differential gainUsing the dominant-pole model for the op-amp,A d (s) ¼whereA o is the dc gainv a is the dominant poleGB is the gain-bandwidth product of the op-ampInserting Equation 11.79 into Equation 11.78 givesGBs þ v a¼ A ov as þ v a(11:79)GBK ¼s þ v a ð1 þ A o =K o Þ GB(11:80)s þ GB=K oThe approximation of the K expression is valid provided A o K o . The magnitude and phase of Equation11.80 arejK( jv) j ¼GBq ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi(11:81)v 2 þ ðGB=K o Þ 2andarg [K( jv)] ¼ tan 1 vGB K o(11:82)Note that for v > GB=K o , Equations 11.81 and 11.82 may be approximated byandjK( jv) j K o (11:83)arg [K( jv)] v GB K o (11:84)
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Passive, Active,and DigitalFilters
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The Circuits and Filters HandbookTh
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ContentsPreface ...................
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PrefaceAs circuit complexity contin
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ContributorsPhillip E. AllenSchool
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IPassive FiltersWai-Kai ChenUnivers
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1General Characteristicsof FiltersA
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General Characteristics of Filters
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1-12 Passive, Active, and Digital F
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2-2 Passive, Active, and Digital Fi
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Approximation 2-9K(ω)Large nSmall
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Approximation 2-132π21φ = cos -1
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Approximation 2-15This result is us
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Approximation 2-19Butterworth; put
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Approximation 2-21This however impl
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Approximation 2-23TABLE 2.3 Bessel
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Approximation 2-25R mn (ω)b + εbb
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Approximation 2-27is a measure of t
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Approximation 2-29Recall, now, the
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Approximation 2-31TABLE 2.4 Zeros o
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Approximation 2-33References1. A. M
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4Sensitivityand SelectivityIgor M.
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Sensitivity and Selectivity 4-34.3
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Sensitivity and Selectivity 4-5Beca
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Sensitivity and Selectivity 4-7Simi
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Sensitivity and Selectivity 4-9comp
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Sensitivity and Selectivity 4-11In
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Sensitivity and Selectivity 4-13and
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Sensitivity and Selectivity 4-154.8
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Sensitivity and Selectivity 4-17cha
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Sensitivity and Selectivity 4-19Tak
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Sensitivity and Selectivity 4-21I p
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Sensitivity and Selectivity 4-23Att
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Sensitivity and Selectivity 4-25 In
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Sensitivity and Selectivity 4-27the
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Sensitivity and Selectivity 4-29is
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Sensitivity and Selectivity 4-311.
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5Passive Immittancesand Positive-Re
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Passive Immittances and Positive-Re
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6Passive CascadeSynthesisWai-Kai Ch
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Passive Cascade Synthesis 6-3not gr
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Passive Cascade Synthesis 6-5degree
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Passive Cascade Synthesis 6-7M < 0L
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Passive Cascade Synthesis 6-9LN AFI
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Passive Cascade Synthesis 6-11ζCN
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Passive Cascade Synthesis 6-13the d
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Passive Cascade Synthesis 6-15The e
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7Synthesis of LCM andRC One-Port Ne
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Synthesis of LCM and RC One-Port Ne
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V g-V g-9-8 Passive, Active, and Di
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10Design of BroadbandMatching Netwo
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Design of Broadband Matching Networ
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Page 226 and 227: 11Low-Gain Active FiltersPhillip E.
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Page 252 and 253: Low-Gain Active Filters 11-27TABLE
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14The CurrentGeneralizedImmittance
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The Current Generalized Immittance
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15High-Order FiltersRolf SchaumannP
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High-Order Filters 15-3V inV o2V oi
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High-Order Filters 15-5Choosing the
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High-Order Filters 15-7where we def
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High-Order Filters 15-9where we int
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High-Order Filters 15-11where s is
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High-Order Filters 15-1315.4.1 Sign
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High-Order Filters 15-15Ri2R 4V oR
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High-Order Filters 15-17Notice that
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High-Order Filters 15-19v i g i(α
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High-Order Filters 15-21TABLE 15.1
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High-Order Filters 15-23R a1 ¼ ^C
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High-Order Filters 15-25I 1 1V 1 sk
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High-Order Filters 15-27664154015.2
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16Continuous-TimeIntegrated Filters
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Continuous-Time Integrated Filters
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17Switched-CapacitorFiltersJose Sil
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Switched-Capacitor Filters 17-3C SC
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Switched-Capacitor Filters 17-5For
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Switched-Capacitor Filters 17-7φ 2
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Switched-Capacitor Filters 17-9A 3
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Switched-Capacitor Filters 17-11whe
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Switched-Capacitor Filters 17-1317.
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Switched-Capacitor Filters 17-15C i
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Switched-Capacitor Filters 17-1717.
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Switched-Capacitor Filters 17-19The
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Switched-Capacitor Filters 17-21Dur
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Switched-Capacitor Filters 17-23sig
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Switched-Capacitor Filters 17-25C 1
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Switched-Capacitor Filters 17-27φC
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Switched-Capacitor Filters 17-29for
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Switched-Capacitor Filters 17-31If
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Switched-Capacitor Filters 17-33FIG
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Switched-Capacitor Filters 17-35CH1
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IIIDigital FiltersRashid AnsariUniv
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18FIR FiltersM. H. ErNanyang Techno
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FIR Filters 18-3Consequently,tan (v
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FIR Filters 18-5TABLE 18.1Frequency
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FIR Filters 18-7H d (e jω )1To und
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FIR Filters 18-90-10-20Amplitude re
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FIR Filters 18-110-5-10Amplitude re
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FIR Filters 18-130-20Amplitude resp
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FIR Filters 18-15TABLE 18.2Spectral
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FIR Filters 18-17If it were possibl
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FIR Filters 18-19The alternation th
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FIR Filters 18-21respectively, and
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FIR Filters 18-23Rejection of super
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FIR Filters 18-25The selective step
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FIR Filters 18-27TABLE 18.4 Impulse
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FIR Filters 18-29selective step-by-
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FIR Filters 18-31Odd filter lengthM
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FIR Filters 18-33and1a 1 ¼ ~c 02 ~
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FIR Filters 18-35a useful property
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FIR Filters 18-37with the number of
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FIR Filters 18-39F(z L )z −LN F /
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FIR Filters 18-411F(Lω)G 1 (ω)0 0
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FIR Filters 18-43TABLE 18.11Algorit
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FIR Filters 18-451N ove ¼ N optL
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FIR Filters 18-47TABLE 18.13 Implem
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FIR Filters 18-494. If r ¼ R, then
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FIR Filters 18-51In this case, the
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FIR Filters 18-53Estimated orders11
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FIR Filters 18-550Amplitude (db)−
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FIR Filters 18-57In the above, the
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FIR Filters 18-59TABLE 18.15Data fo
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FIR Filters 18-614. Y. C. Lim and Y
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19-10 Passive, Active, and Digital
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20Finite WordlengthEffectsBruce W.
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Finite Wordlength Effects 20-3the q
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Finite Wordlength Effects 20-5From
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Finite Wordlength Effects 20-7In ge
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Finite Wordlength Effects 20-9To ob
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Finite Wordlength Effects 20-11Howe
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Finite Wordlength Effects 20-13wher
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Finite Wordlength Effects 20-15 y(4
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Finite Wordlength Effects 20-17j1.0
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Finite Wordlength Effects 20-1921.
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23Two-DimensionalIIR FiltersA. G. C
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Two-Dimensional IIR Filters 23-323.
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Two-Dimensional IIR Filters 23-5a 1
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Two-Dimensional IIR Filters 23-7x(n
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Two-Dimensional IIR Filters 23-9+π
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Two-Dimensional IIR Filters 23-11TA
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Two-Dimensional IIR Filters 23-13wh
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Two-Dimensional IIR Filters 23-15ω
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Two-Dimensional IIR Filters 23-17x
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Two-Dimensional IIR Filters 23-19St
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Two-Dimensional IIR Filters 23-21In
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Two-Dimensional IIR Filters 23-23an
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Two-Dimensional IIR Filters 23-25-1
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Two-Dimensional IIR Filters 23-2711
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Two-Dimensional IIR Filters 23-29is
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Two-Dimensional IIR Filters 23-33Co
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Two-Dimensional IIR Filters 23-35In
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Two-Dimensional IIR Filters 23-37f
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Two-Dimensional IIR Filters 23-39If
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Two-Dimensional IIR Filters 23-41TA
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Two-Dimensional IIR Filters 23-43f
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Two-Dimensional IIR Filters 23-45St
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241-D MultirateFilter BanksNick G.
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1-D Multirate Filter Banks 24-324.2
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1-D Multirate Filter Banks 24-5Subs
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1-D Multirate Filter Banks 24-7y 00
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1-D Multirate Filter Banks 24-9Haar
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1-D Multirate Filter Banks 24-11H k
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1-D Multirate Filter Banks 24-13Now
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1-D Multirate Filter Banks 24-1510h
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1-D Multirate Filter Banks 24-17Equ
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1-D Multirate Filter Banks 24-191Da
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1-D Multirate Filter Banks 24-211An
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1-D Multirate Filter Banks 24-231Ne
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1-D Multirate Filter Banks 24-25dur
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1-D Multirate Filter Banks 24-27Rec
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1-D Multirate Filter Banks 24-29pre
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1-D Multirate Filter Banks 24-31The
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1-D Multirate Filter Banks 24-332An
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1-D Multirate Filter Banks 24-352.
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1-D Multirate Filter Banks 24-39by
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1-D Multirate Filter Banks 24-41x0
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1-D Multirate Filter Banks 24-43pri
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1-D Multirate Filter Banks 24-45The
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1-D Multirate Filter Banks 24-47Two
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1-D Multirate Filter Banks 24-49" #
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1-D Multirate Filter Banks 24-51Tre
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ω 1πω 1π25-8 Passive, Active, a
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26Nonlinear FilteringUsing Statisti
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Nonlinear Filtering Using Statistic
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27Nonlinear Filtering forImage Deno
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Nonlinear Filtering for Image Denoi
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IN-2Indeximpulse invariance method,
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IN-4Indexprescribed specification,2
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IN-6Indexfilter rank ordering, 2-32
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IN-8Indexpassband and stopband ripp
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IN-10Indexstate-space filter realiz
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IN-12Indexnonessential singularitye
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IN-14Indexreal-valued weights andop
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IN-16Indexbaseband communication,26
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IN-18Indexarbitrary specificationCh
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IN-20IndexVoltage-controlled curren
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