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

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Nonlinear Filtering for Image Denoising 27-2527.3.4 Denoising AlgorithmThe denoising algorithm works in three steps: forward DPT, adaptive thresholding, and inverse DPT.The coefficients of D forward DPT of the image volume are computed using the algorithm outlined inSection 27.3.3. Since the presence of additive Gaussian white noise means that almost all the DPTcoefficients are affected by it, soft thresholding would reduce the contribution of noise to the restoredimage volume. Based on the assumption that the coefficients relatively small in magnitude at eachresolution (i.e., below a certain threshold) are most probably due to the noise variation, coefficients withmagnitude above a certain threshold are kept while the remaining ones are discarded. The inverse DPT,therefore, provides an estimation of the original uncorrupted image volume.The choice of threshold is crucial to the performance of this type of transform domain denoising.Donoho and Johnstone [44] have shown that an adaptive threshold u given bypu ¼ sffiffiffiffiffiffiffiffiffiffiffiffi2 log n(27:44)is an asymptotically optimal choice for threshold value when denoising a 1-D noisy signal, wheren denotes the number of samples in the signal and s is standard deviation of the additive Gaussianwhite noise. Our experiments showed that using an adaptive threshold for coefficients at differentresolutions gives better denoising results as compared to using same threshold value for transformcoefficients at all resolutions. We use threshold value u i for coefficients at level i of the pyramidas given bypffiffiffiffiffiffiffiffiffiffiffiffiffiffiu i ¼L(s) 2 log n i , (27:45)wheren i denotes the number of pixels at level i of the pyramidL(s) is a suitably chosen function of sThe following expression for L(s) was empirically chosen for our experiments:where a, b 2
27-26 Passive, Active, and Digital Filterst12010080604020(a)12010080y604020 20406080x100120t12010080604020(b)12010080y604020 20406080x100120FIGURE 27.16(b) planelets.Nonlinear approximation of a video sequence containing a moving circle using (a) wavelets andapproximation of a video sequence. Moreover, the approximation can be made to be adaptive to thelocal scale of the planar surfaces.27.4 3-D Wavelet PacketsThe case for thresholding in spatiotemporal wavelet domain is supported by the fact that certain errors inmotion estimation can be overcome by including the temporal direction in the realm of wavelet domain.Recent attempts to solve the video restoration problem have included combined spatial and temporalwavelet denoising [45], and the use of thresholding in nonseparable transform domains, such as oriented3-D ridgelets [46] and 3-D complex wavelets [47].Although wavelet shrinkage performs significantly better than most other commonly used denoisingmethods, visual quality of the restored video can sometimes suffer from ringing type of artifacts, valleys
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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 24-27Rec
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1-D Multirate Filter Banks 24-29pre
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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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Page 764 and 765: 27Nonlinear Filtering forImage Deno
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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
Page 829 and 830: IN-10Indexstate-space filter realiz
Page 831 and 832: IN-12Indexnonessential singularitye
Page 833 and 834: IN-14Indexreal-valued weights andop
Page 835 and 836: IN-16Indexbaseband communication,26
Page 837 and 838: IN-18Indexarbitrary specificationCh
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IN-20IndexVoltage-controlled curren
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