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

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General Characteristics of Filters 1-13By lettingjv z i ¼ M zi e jc z i (1:14)jv p i ¼ M pi e jc p i (1:15)we obtainandjM(v) ¼ H 0j Q Mi¼1 M z iQNi¼1 Mmip i(1:16)u(v) ¼ arg H 0 þ XMc zii¼1X Ni¼1m i c pi(1:17)where arg H 0 ¼ p if H 0 is negative.The gain and phase shift M(v) and u(v) for some frequency v ¼ v i can be determined graphically byusing the following procedure:1. Mark the zeros and poles of the filter in the s plane.2. Draw the phasor s ¼ jv i , where v i is the frequency of interest.3. Draw a phasor of the type in Equation 1.14 for each simple zero of H(s).4. Draw m i phasor of the type in Equation 1.15 for each pole of order m i .5. Measure the magnitudes and angles of the phasors in steps 3 and 4 and use them in Equations 1.16and 1.17 to calculate the gain M(v i ) and phase shift u(v i ), respectively.The amplitude and phase responses of a filter can be determined by repeating the preceding procedurefor frequencies v ¼ v 1 , v 2 , . . . , in the range 0 to 1. The procedure is illustrated in Figure 1.4.It should be mentioned that the modern approach for the analysis of filters is through the use of themany circuit analysis programs such as SPICE.* Nevertheless, the above graphical method is of interestand merits consideration for two reasons. First, it illustrates some of the fundamental properties of filters.Second, it provides a certain degree of intuition about the expected amplitude or phase response of afilter. For example, if a filter has pole close to the jv axis, then as v approaches the neighborhood of thepole, the magnitude of the phasor from the pole to the jv axis decreases rapidly to a very small value andthen increases as v increases above this value. As a result, the amplitude response will exhibit a large peakin the frequency range close to the pole. On the other hand, a zero close to or on the jv axis will lead to anotch in the amplitude response when v is in the neighborhood of the zero.Other situations are of interest, for example, if the poles of a filter are located in a band of the splane below the horizontal line s ¼ v c and its zeros are located above this line, then the filter will passlow-frequency and attenuate high-frequency components since M zi < M pi if v > v c for all i. Such a filteris said to be a low-pass filter. If the zeros are located below the line s ¼ v c and the poles above it, thenthe filter will pass high-frequency and attenuate low-frequency components, i.e., the filter will be ahigh-pass one.* See Chapter 8 of Computer Aided Design and Design Automation, contribution of J.G. Rollins.
1-14 Passive, Active, and Digital Filtersjωs planejω i – p 1 = M p1 e jψ p 1 jω ijω i – z 1 = M z 1e jψ z 1p 1ψ z1z 1ψ p3M p2p 3p 2σz 2FIGURE 1.4Graphical method for the evaluation of the frequency response.1.4.3 Loss FunctionQuite often, it is desirable to represent a filter in terms of its loss function. Consider a filter represented bythe voltage transfer functionV o (s) N(s)¼ H(s) ¼V i (s) D(s)whereV i (s) and V o (s) are the Laplace transforms of the input and output voltages, respectivelyN(s) and D(s) are polynomials in sThe loss (or attenuation) of the filter in decibels is defined asA(v) ¼ 20 log V i( jv)V o ( jv) ¼ 20 log 1jH( jv) j ¼ 10 log L v2 (1:18)whereL v 2 ¼1H( jv)H( jv)A(v) as a function of v is the loss characteristic.
Page 2 and 3: Passive, Active,and DigitalFilters
Page 4 and 5: The Circuits and Filters HandbookTh
Page 6 and 7: ContentsPreface ...................
Page 10: PrefaceAs circuit complexity contin
Page 14 and 15: ContributorsPhillip E. AllenSchool
Page 16 and 17: IPassive FiltersWai-Kai ChenUnivers
Page 18 and 19: 1General Characteristicsof FiltersA
Page 20 and 21: General Characteristics of Filters
Page 29: 1-12 Passive, Active, and Digital F
Page 46: General Characteristics of Filters
Page 49 and 50: 2-2 Passive, Active, and Digital Fi
Page 56: Approximation 2-9K(ω)Large nSmall
Page 60 and 61: Approximation 2-132π21φ = cos -1
Page 62: Approximation 2-15This result is us
Page 66 and 67: Approximation 2-19Butterworth; put
Page 68 and 69: Approximation 2-21This however impl
Page 70 and 71: Approximation 2-23TABLE 2.3 Bessel
Page 72 and 73: Approximation 2-25R mn (ω)b + εbb
Page 74 and 75: Approximation 2-27is a measure of t
Page 76 and 77: Approximation 2-29Recall, now, the
Page 78 and 79: Approximation 2-31TABLE 2.4 Zeros o
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Approximation 2-33References1. A. M
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3-2 Passive, Active, and Digital Fi
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3-10 Passive, Active, and Digital F
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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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IIActive FiltersWai-Kai ChenUnivers
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11Low-Gain Active FiltersPhillip E.
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Low-Gain Active Filters 11-3The dam
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Low-Gain Active Filters 11-5at a fr
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Low-Gain Active Filters 11-7+RK++CK
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Low-Gain Active Filters 11-9R 2+R 1
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Low-Gain Active Filters 11-11For th
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Low-Gain Active Filters 11-13The se
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Low-Gain Active Filters 11-15Y 1H22
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Low-Gain Active Filters 11-17R 2+R
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Low-Gain Active Filters 11-19To con
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Low-Gain Active Filters 11-21+10k 1
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Low-Gain Active Filters 11-23TABLE
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Low-Gain Active Filters 11-25The ph
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Low-Gain Active Filters 11-27TABLE
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Low-Gain Active Filters 11-29I n1E
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Low-Gain Active Filters 11-3150 nVS
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12Single-AmplifierMultiple-Feedback
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Single-Amplifier Multiple-Feedback
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13-10 Passive, Active, and Digital
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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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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 23-35In
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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 24-17Equ
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1-D Multirate Filter Banks 24-191Da
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1-D Multirate Filter Banks 24-231Ne
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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 24-39by
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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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