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

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Nonlinear Filtering for Image Denoising 27-15605550PSNR4540353025PCT–IIPCT–XDCT–IIFourier transformFCT0 5 10 15 20 25 30 35 40 45 50Coefficient percentageFIGURE 27.7Illustrative results for nonlinear approximation on fp.110100908070PSNR605040PCT–IIPCT–X30DCT–IIFourier transformFCT200 5 10 15 20 25 30 35 40 45 50Coefficient percentageFIGURE 27.8Illustrative results for nonlinear approximation on line.
27-16 Passive, Active, and Digital Filterscoefficients. The DCT shows the ghosting artifact on two different orientations, the FFT has two ghostlines appearing on the reconstruction. The PCT-II, on the other hand, due to the boundary extensionbeing assumed on the Radon slices, shows only one significant ghost line. The ghosting artifact is furtherreduced in PCT-X’s reconstruction.27.2.6 Polar Cosine PacketsAs previously discussed, the Radon transform can reduce the PCT into a matter of performing the cosinetransform on Radon slices. This also makes it possible to analyze directional features other thansinusoidal ridges. This is achieved by taking the transform in separate spatial windows. Local trigonometricbases proposed by Coifman and Meyer [30] and by Malvar [31] use smooth window functions tosplit the signal and to fold overlapping parts back into the original pieces so that the orthogonality ispreserved. This treatment can avoid the discontinuity artifacts caused by a rectangular window, whileintroducing no redundancy.The local cosine basis is composed of basis functions of the formsffiffiffiffiffiffi 2w p,k (t) ¼ w p (t) cos p k þ 1 t cp: (27:31)jI p j2 jI p jThe Cosine-VI basis is used and modulated by a window function w p (t) which lies on an interval[a p 1 , a p ] with c p ¼ a p þ a p 1 )=2, and jI p j¼c pþ1 c p being the length of the window, with theoverlapping part included. With a careful choice of the window (see Ref. [15]), the set fa p gR formsa partition of unity and the local cosine basis associated to such partition is said to form a library oforthonormal bases usually referred to as the cosine packets.The polar cosine packets can be implemented by placing the 1-D cosine packets on the Radon slices;the operator is denoted asPf [p, k, u] ¼hRf [t, u], w p,k [t]i: (27:32)Unfortunately, due to its implementation, it is not possible to construct similar polar cosine packets withthe PCT-X.27.2.7 Best Basis SelectionThe arbitrary choice over the library of local trigonometric bases over a compact interval U is of anextremely large range. To seek a feasible ‘‘best basis,’’ the library of cosine packets is reduced to onlytaking dyadically partitioned decomposition of U only. This organization is depicted schematically inFigure 27.9. Then I 00 is a cosine basis on the entire U and I p,s will correspond to the local cosine basis overinterval p of the 2 s intervals at level s of the tree. The best basis can be found by induction on s.Let B p,s denote the cosine basis vectors corresponding to interval I p,s , and A p,s be the best basis. Fors ¼ 0, the best basis A p,0 ¼ B p,0 , otherwiseA p,sþ1 ¼ B p,sþ1 if M(B p,sþ1 x) < M(A 2p,s x) þM(A 2pþ1,s x),A 2p,s A 2pþ1,s otherwise.(27:33)
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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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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 23-29is
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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 24-39by
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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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Page 730 and 731: 26Nonlinear FilteringUsing Statisti
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Page 764 and 765: 27Nonlinear Filtering forImage Deno
Page 766 and 767: Nonlinear Filtering for Image Denoi
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Page 821 and 822: IN-2Indeximpulse invariance method,
Page 823 and 824: IN-4Indexprescribed specification,2
Page 825 and 826: IN-6Indexfilter rank ordering, 2-32
Page 827 and 828: 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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