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

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Switched-Capacitor Filters 17-19The design of the operational amplifier is strongly dependent on the application. For high-frequencycircuits, the folded cascode op-amp is suitable, but the cascode transistors limit the swing of the signals atthe output stage. If large output voltage swing is needed, complementary stages are desirable. To illustratethe design trade-offs involved in the design of a low-voltage OTA, let us consider the folded cascode OTAof Figure 17.11. For low-voltage applications and small signals, the transistors have to be biased with verylow V DSAT (¼V GS V T ).For the case of supply voltages limited to 0.75 V and V T ¼ 0.5 V, V DSAT1 þ V DSAT6 must be lowerthan 0.25 V, otherwise the transistor M 6 goes to the triode region. For large signals, however, thevariations of the input signal produce variations at the source voltage of M 1 . It is well knownthat linear range of the differential pair is of the order of 1.4 V DSAT1 . Hence, if the noninvertinginput of the OTA is connected to the common-mode level V CM , for proper operation of the OTA inputstage (see Figure 17.11) it is desirable to satisfyV CM V T VSS > 1:4V DSAT1 þ V DSAT6 (17:50)It has to be taken into account that the threshold voltage of M 1 increases if an N-well process is used,due to the body effects. In critical applications, PMOS transistors fabricated in a different well withtheir source tied to their own well can be used. Equation 17.50 shows that it is beneficial to select aproper common-mode level V CM to extend the linear range of the amplifier input stage, especially forlow-voltage applications.The dimensioning of the transistors and the bias conditions are directly related to the application. Forinstance, if the SC integrator must slew 1 V into 4 ms and the load capacitor is of the order of 10 pF,the OTA output current must be equal to or higher than 2.5 mA. Typically, for the folded cascodeOTA the dc current of both output and input stages are the same. Therefore, the bias current for M 1 ,M 3 ,M 4 , and M 5 can be equal to 2.5 mA. The bias current for M 2 and M 6 is 5 mA. If V GS1 V T1 is fixed at100 mV the dimensions of M 1 can be computed according to the required small signal transconductance.Similarly, the dimension of the other transistors can be calculated, most of them designed to maximizethe output swing and dc gain. A very important issue in the design of low-voltage amplifiers is thereference voltage. In the folded cascode of Figure 17.11, the values of the reference voltages V R1 and V R2must be optimized for maximum output swing. OTA design techniques are fully covered in Refs. [11]and [13].17.5.2 Analog SwitchesFor low-voltage applications, the highest voltage that can be processed is limited by the analogswitches rather than by the op-amps. For a single NMOS transistor, the switch resistance is approximatelygiven by1R DS ¼Wm n C OX L (V GS V T )(17:51)where m n and C OX are technological parameters. According to Equation 17.51, the switch resistanceincreases further when V GS approaches to V T . This effect is shown in Figure 17.15 for the caseV DD ¼ V SS ¼ 0.75 V and V T ¼ 0.5 V. From this figure, the switch resistance is higher than 300 kVfor input signals of 0.2 V. However, for a drain-source voltage higher than V GS V T the transistorsaturates and does not behave as a switch anymore. This limitation clearly reduces further the dynamicrange of the SC circuits.A solution for this drawback is to generate the clocks from higher voltage supplies. A simplifieddiagram of a voltage doubler is depicted in Figure 17.16a. During the clock phase f 1 , the capacitor C 1 ischarged to V DD and during the next clock phase its negative plate is connected to V DD . Hence, at the
17-20 Passive, Active, and Digital Filters1612Switch resistance (×100 K)8400.00 0.05 0.10 0.15 0.20 0.25V in (v)FIGURE 17.15Typical switch resistance for an NMOS transistor.φ΄2V DDφ 1CM V C 38yC pφ 1φ 2M 4 M 3V oφ 1C 1 C Loadφ΄2V OLoadM 7 V xφ 1C 2φ΄2M 6 M 5V SSM 2 M 1V DD(a)φ 2φ 1V SS(b)V SSFIGURE 17.16Voltage doubler. (a) Simplified diagram and (b) transistor level diagram.beginning of f 2 , the voltage at the top plate of C 1 is equal to 2V DD V SS . After several clockcycles, if C LOAD is not further discharged, the charge is recombined leading to an output voltage equalto 2V DD – V SS . A practical implementation for an N-well process is shown in Figure 17.16b.In this circuit, the transistors M 1 ,M 2 ,M 3 , and M 4 behave as the switches S 1 ,S 2 ,S 3 , and S 4 respectively,of Figure 17.16a. While for M 1 and M 2 the normal clocks are used, special clock phases are generated forM 3 and M 4 because they drive higher voltages. The circuit operates as follows.
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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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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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Page 418 and 419: IIIDigital FiltersRashid AnsariUniv
Page 420 and 421: 18FIR FiltersM. H. ErNanyang Techno
Page 422 and 423: FIR Filters 18-3Consequently,tan (v
Page 424 and 425: FIR Filters 18-5TABLE 18.1Frequency
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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 23-29is
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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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