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One of the many contributions of Prof. Fettweis was the invention of wave digital filters. These filters are obtained from classical RLC filters, in particular doubly terminated lossless two-ports, by using some transformations. Namely, the voltages and currents in the circuit elements are transformed into wave-variables and then a bilinear transformation is performed. If the wave transformation is performed appropriately it results in a realizable digital filter structure which furthermore enjoys a number of robustness properties such as low passband sensitivity, low roundoff noise, and freedom from limit cycle oscillations. Prof. Fettweis and his colleagues also showed that these properties are due to the inheritence of passivity properties from the continuous-time domain into the digital filter domain. Subsequent to this landmark work, a number of researchers worked on the problem of obtaining robust digital filter structures without starting from continuoustime circuits. One of these is the structurally bounded or structurally passive class of digital filters. These structures are based on inducing structural passivity directly into the implementation and are therefore simpler, both conceptually and from a practical viewpoint. They are also more general and lead to new structures which have no natural connection to electrical circuits. This paper gives an overview of some of these developments.

For part I see ibid., vol. 43, no. 6, p. 422-33 (1996). The concept of the nonuniform discrete Fourier transform (NDFT) is extended to two dimensions to provide a basic framework for nonuniform sampling of 2-D sequences in the frequency domain. The 2-D NDFT of a sequence of size N/sub 1//spl times/N/sub 2/ is defined as samples of its 2-D z-transform evaluated at N/sub 1/N/sub 2/ distinct points located in the 4-D (z/sub 1/, z/sub 2/) space. These points are chosen appropriately so that the inverse transform exists. We discuss two special cases in which the choice of the sampling points is constrained so that the 2-D NDFT matrix is guaranteed to be nonsingular, and the number of operations required for computing its inverse is reduced, The 2-D NDFT is applied to nonuniform frequency sampling design of 2-D finite-impulse-response (FIR) filters. Nonseparable filters with good passband shapes and low peak ripples are obtained. This is illustrated by design examples, in which 2-D filters with various shapes are designed and compared with those obtained by other existing methods.

Block digital filtering has been suggested to increase the parallelism of computation and to reduce the computational complexity of digital filtering systems. In this paper the block processing concept is generalized by considering overlapped input and/or output blocks. As an overlapped block digital filter is, in general, a shift-varying system, the conditions for its shift-invariant operation have been developed. These conditions have been exploited to derive computationally efficient shift-invariant block structures. Two types of fast FIR filtering algorithms using the overlapped block filter structures are derived. One is based on the adaptation of fast short-length linear convolution algorithms and the other is based on DFT algorithms. These algorithms not only reduce the computational complexity of filtering operations but also offer modular and parallel structures. Finite wordlength effects of FIR filters implemented using the overlapped block filter structure are also investigated.

This paper re-examines modulated polyphase filter banks which use reverse-time subfilters to achieve perfect reconstruction and studies their performance for image coding when used to form a wavelet decomposition. To code the wavelet coefficients, we use the embedded zerotree wavelet (EZW) algorithm developed by Shapiro (1993) which is reasonably simple and yet achieves very good rate-distortion performance. The problem of eliminating filter transients is thoroughly studied and optimal results are derived in both the absence and presence of subband coefficient quantization. Using this analysis as a starting point, we develop a new method of coding the filter states (required to eliminate edge transients) for transmission to the receiver which efficiently exploits interscale redundancy and is easily incorporated into the zerotree algorithm. Comparing this direct transmission method to circular convolution, we find that it achieves superior rate-distortion performance in a wide range of cases. Coding comparisons between two infinite impulse response (IIR) wavelets and a number of biorthogonal wavelets are presented. These comparisons indicate that the performance of the polyphase allpass wavelet is comparable to that of the best finite impulse response (FIR) biorthogonal wavelets with considerably reduced computational complexity.

In this correspondence, we present a stochastic convergence analysis of a second-order adaptive IIR notch filter. The approach is based on a linearization of the gradient in the vicinity of the optimal solution. Expressions for stability bounds on the algorithm step size and the steady-state coefficient variance are derived. These closed-form analytical results are verified by computer simulations for different signal and noise conditions. >

A new method is presented for the fast and efficient design of one-dimensional (1D) and two-dimensional (2D) linear phase FIR filters. In this approach, the concept of structural subband decomposition of 1D and 2D sequences is applied to an improved method for frequency-sampling FIR filter design. Using this decomposition the filter is implemented as a parallel connection (bank) of sparse subfilters cascaded with interpolators. An algebraic relationship is then developed to determine the frequency samples of the subband filters from the original specified frequency samples. Filter designs based on various types of interpolators derived from transform matrices such as the Hadamard, binomial, and DCT are investigated. Significant computational savings arise from discarding subbands that contribute little to the overall frequency response and selectively quantizing the wordsize of the coefficients of the remaining subfilters. In addition to implementation advantages over traditional techniques, the proposed method enables a more accurate specification of filter design parameters, near optimal responses, and a design time considerably faster than that of the Parks-McClellan algorithm. >

In this paper, a new structure for the detection of sinusoids using adaptive IIR notch filters and multirate techniques is presented. By using the frequency enhancement property of the decimation in time process, the proposed structure avoids the use of almost unity radius notch filters. A stochastic analysis of the convergence properties of the proposed multirate IIR notch filter structure is discussed. The analysis verifies the low adaptation coefficient variance of the proposed structure, and the small bias in the frequency estimates of multiple sinusoidal signal. Computer simulations show the superior performance of the proposed structure for the detection of closely-spaced sinusoids and tracking of nonstationary sinusoidal signals. >

An adaptive structure based on a generalized structural subband decomposition of FIR (finite-impulse-response) filters is presented. The proposed structure implements an adaptive FIR filter of length N as a parallel connection of L branches, with each branch composed of a cascade of a fixed interpolator and a sparse adaptive subfilter containing at least L nonzero coefficients. There is no sampling rate alteration in this structure, and therefore no problems with aliasing occur. The interpolators are implemented by a computationally efficient transform (e.g., DCT, DFT). The proposed structure presents superior convergence performance for colored input signals when compared to the conventional direct-form LMS (least-mean-square) structure, with a very small increase in the number of operations. The advantages of using the subband structure in the adaptive line enhancer, acoustic echo canceller, and channel equalizer applications are shown through computer simulations. >

LMS (least-mean-square) adaptive filtering algorithms using FIR (finite-impulse-response) filter structures based on structural subband decomposition are developed. It is shown that the subband decomposition is equivalent to transformation of input data by orthogonal matrices of which the Walsh-Hadamard transform (WHT) is a special case. The proposed method is a generalization of WHT-based transform domain adaptive filtering, which is known to enhance the convergence speed of adaptive filters. It is also shown that the interpolator network of the subband structure is a fast implementation of the required transform and is therefore attractive from a practical standpoint. The convergence properties of subband FIR adaptive filters are studied for system identification applications. The results demonstrate the advantages of the proposed structure compared to conventional adaptive filters. >

A certain class of frequency selective digital IIR filters, including the classical Butterworth, Chebyshev and elliptic filters, can be realized as a parallel connection of two real or complex conjugate allpass filter. In this paper, a generalized structure where the allpass branches include arbitrary real or complex weighting constants is discussed. Applications of these generalized doubly complementary filters include gain equalizers, digital filters with multilevel magnitude response, and sharpening the amplitude response of digital filters realized as a cascade of identical filter stages.

In this letter we make use of a novel multiple feedback active RC filter structure in which the feedback path is realized in a parallel form. The parallel feedback structure was originally applied to the design of low-round-off-noise digital filters with dynamic range control. Most of these attractive properties result from the appropriate use of several degrees of freedom that are available in the design process. In the proposed active RC filter implementation scheme we show how to use these degrees of freedom to minimize the sensitivity measure while satisfying the dynamic range constraints

A new method for changing the cut-off frequency of infinite impulse response (IIR) digital filters with a single parameter is derived. the method is based on the use of the Taylor series expansion of the lowpass-to-lowpass frequency transformation. the filter structure is a parallel connection of real or complex allpass sections. the tuning range is several octaves for narrowband filters. By taking also the complementary output, a power-complementary filter pair with tunable crossover frequency is readily obtained. Tunable centre frequency and bandwidth are obtained by incorporating a special lowpass-to-bandpass transformation into the structure. Design examples and a description of a signal processor implementation are included.

A new class of linearly tapered window, obtained by the convolution of a moving average filter and a running sum filter of unequal lengths, is introduced. The sidelobe rejection of the new window is between that of the rectangular and the Hann windows, and can be varied as a function of the lengths of the two convolving filters. We study the properties of the new window and provide empirical formulas for the sidelobe rejection and the mainlobe width. We propose rules for finite impulse response (FIR) filter design using the new window and show that a significant reduction in the filter length can be obtained as compared to that of the filter designed using the Hann window.

Two adaptive filter structures using filter banks are derived. The first structure, based on the transform domain adaptive algorithm, results in significant fast convergence rate at the cost of few more operations the second one is a frequency sampling adaptive filter in which the filter bank outputs are decimated by a factor such that the computational complexity is minimized. Computer simulations are included to illustrate the performances of the proposed structures.

A digitally programmable switched-capacitor equalization filter is presented. The design is entirely carried on the z-domain, which leads to exact transfer functions. The filter uses a structurally all pass section as a basic building block, resulting in a robust equalizer with low sensitivities with respect to capacitor ratios. Experimental results obtained with a discrete prototype are included.

Rabiner and Goldl have outlined an approach to the implementation of one-dimensional FIR digital filters using only one multiplier. This direct implemen- tation uses shift registers to store input values and either shift registers or read-only-memories (ROM's) to store the filter coefficients. Through appropriate shifting, the correct input and filter coefficient pair are presented to the multiplier inputs. These products are accumulated by an adder and a storage register. The main advantage of this technique is that only one multiplier is needed regardless of filter order thus reducing cost and power requirements.

The last two authors introduced a special class of linear-phase FIR hers, called multiple-branch FIR lters for sampling rate conversion. To minimize the multiplication rate of the aforementioned class of lters, the authors proposed a systematic technique, based on nonlinear (quadratic) optimization. This paper presents an improvement over the proposed approach through additional constraints in the optimization routine.

A unified approach to the efficient realization of FIR adaptive digital filters in both the time and frequency domains is presented. It is shown that previously published frequency domain implementations are contained within this unified approach. It is further shown that various combinations of implementations are possible, and that in working with data streams, care must be taken in using overlap-save and overlap-add sectioning procedures for proper frequency domain implementations.

A microprocessor-based digital filter laboratory station to provide hands-on experience to the students in the design of digital filters is described. The unit is centered around an 8080A microprocessor which can be employed programmatically by the user to interconnect the various modules comprising a digital filter and to experimentally evaluate their characteristics. This flexible laboratory station allows the student to conduct a variety of experiments in the fundamentals of digital signal processing and introductory digital filter design based on the Peled-Liu (Croisier et-al) algorithm.

Efficient computation method for the recursive digital filtering is studied in the multi-processor environment. The method solves the dependency problem by separate computations of the particular and transient solutions. The throughput of the algorithm increases linearly with the number of processors, making it possible to increase the throughput effectively by using multiple number of processors. The implementations of the algorithm using a vector-processor and a multiprocessor in a ring network are also studied.

According to the sampling theorem, a faster sampling rate is required in order to process signals containing high frequency components. The processing rate is restricted by the highest operating speed of devices available. This paper presents the design of N-path parallel processing technique which would overcome the speed limitation of present devices. The transfer function of N-path digital filter is shown to be H(zN), where H(z) is the transfer function of each component filter block. This implies that the overall magnitude response of N-path digital filter is a frequency scaled version of that of component filter. In the proposed paper, a scheme to cancel out the unwanted passbands by cascading several N-path filters is first discussed. Then the design procedure of N-path filter from given specification is illustrated using simple example.

This paper presents a formal procedure for determining the state space representations of any digital network consisting of adders, multipliers and delays. Such representations are called state-structures whenever the state variables are exclusively identified to the appropriately chosen internal node variables of the network. In general, the state-structures corresponding to a given network are not unique, and for non-canonic networks, it is sometimes possible to find state-structures for state vectors of the lowest dimension. Procedures for determining such minimal structures are also discussed.

A normalized digital two-pair has unity L p - scaling norms at all pertinent internal nodes and the two output nodes. A simple technique is proposed to derive the normalized filter structure recently forwarded by Gray and Markel. Additional normalized digital two-pairs are also derived.

The hardware implementation of a two-dimensional (2-D) digital filter using Read Only Memory (ROM) is outlined. Specifically, an implementation scheme for a general all pole 2×2 2-D filter is considered here. The provision for the selection of row or columnwise recursion, and the various sequence of operations involved in the actual processing are discussed.

A new type of cascade form structure for digital filtering is proposed, with each building block being a second order section, that satisfies certain passivity properties. This passivity is essentially a "structure-induced" boundedness on the transfer function magnitude, and leads to low passband sensitivity. In addition, the cascade nature ensures low stopband sensitivity, as zeros on the unit circle continue to remain on the unit circle in spite of the quantization. The structure itself is independent of the pole locations and therefore meets a wide range of filtering applications.

Because of the inherent impossibility of factorizing arbitrary 2-D polynomials, all realization techniques for the general 2-D digital transfer function presented so far deal with the realization of such functions as a whole. This paper presents a new realization scheme which is based on realizing multi-input, multi-output subnetworks of multipliers and adders interconnecting 2-D digital subnetworks containing the z- and w-delay elements and possibly multipliers and adders in known configurations. Choise of different digital subnetworks leads to different realizations of the same transfer function. It has also been pointed out that any arbitrary transfer function of the form \Sigma\min{i=0}\max{M} \Sigma\min{j=0} a_{ij}z^{i}w^{j}/\Sigma\min{i=0}\max{M}\Sigma\min{j=0}\max{N} b_{ij}z^{i}w^{j} can always be realized by at most min(2M+N, 2N+M) z- and w-delays.

An efficient three-step method for the design of multiplier-free finite impulse response (FIR) filter is presented. In the first step, the desired filter is realized in the form of an interpolated finite impulse response (IFIR) structure consisting of a cascade of a sparse model filter and an interpolator. In the next step, both sub-filters are approximated by rounding of the filter coefficients. In the final step, the sharpening technique is used to improve the overall magnitude characteristics and to satisfy the given specifications

This paper presents a computer-based method for computing algebraically the pole sensitivities of various second-order digital filter sections. The sensitivity matrix of the pole displacement is derived in a symbolic form using MATLAB. From the sensitivity matrix the variations of pole radius and angle are derived as a function of changes of the parameters of the denominator polynomial and the filter coefficients.

A systematic approach is proposed for designing a class of special linear-phase FIR filters, called multiple branch filters, for sampling rate conversion such that the multiplication rate is minimized. The proposed filters consist of two basic parts. First, as for the polyphase decomposition, the first filter part is implemented using several branches. For the polyphase decomposition, the overall transfer function is constructed using D branches, where D is the sampling rate conversion ratio, and each branch is expressible as z/sup -(k-1)/B/sub k/(z/sup D/) for k=1, 2, /spl middot//spl middot//spl middot/, D. The key idea in reducing the arithmetic complexity in implementing the first filter part is based on the following two facts. First, the first part is expressed as A/sub k/(z)B/sub k/(z/sup D/) for k=1, 2, /spl middot//spl middot//spl middot/, K, where K is only two or three. Second, both the A/sub k/(z)'s are, instead of delay terms z/sup -(k-1)/, and the B(z/sup D/)'s are, instead of nonlinear-phase FIR filters, linear-phase FIR filters with either symmetrical or anti-symmetrical impulse responses, enabling one to exploit the coefficient symmetries in the implementation.

A novel structure for multirate adaptive filtering with lower computational complexity and improved performance of the adaptive algorithm is introduced. It uses auxiliary subbands and a modified filter bank with decimated subbands. It avoids the aliasing distortions encountered in critically decimated overlapping filter banks as well as the spectral gaps in nonoverlapping filter banks. The authors show that this structure has a lower computational complexity than previously reported structures. Computer simulations are included showing the improvement in performance that can be achieved with the new structure operating as an adaptive line enhancer (ALE) compared with the conventional ALE. >

The authors provide an approximate analytical characterization for a wideband lowpass filter realization using the frequency-masking approach, and extend it to the case of wideband bandpass filters. Approximate expressions for the optimal value of the interpolating factor are derived, which minimizes the total arithmetic hardware used in the overall realization. In addition, the authors derive formulae for the total number of adders and multipliers in the overall realization. The proposed two-branch realization is computationally more efficient than the conventional direct-form realization, with a moderate increase in the number of delays. The noise performance of these wideband designs compares very favorably with those of equivalent direct-form realizations. >

A new procedure for checking the stability of 2-D digital filters is proposed. The key part of the test involves construction of related allpass sections of reduced order, stability of which is shown to be equivalent to the stability of the original function. The results are shown to be equivalent to some known stability testing methods in 2-D, but have the advantage of an additional insight gained from the circuit interpretation. Explicit formulas for checking the stability in terms of the filter coefficients are derived for some special cases, and numerical examples are included to clarify the application of the proposed approach. >

A class of linear-phase finite impulse response (FIR) digital filters for sampling rate conversion is introduced. These filters consist of two cascaded parts. The first part is a parallel connection of two or three branches with transfer function of the form A/sub k/(z)B/sub k/) (z/sup D/), where D is the sampling rate conversion ratio. The second part has a transfer function of the form C(z/sup D/). The advantage of these designs is that they provide a significant reduction in the multiplication and addition rates as well as in the number of required multipliers over the equivalent conventional direct-form designs also in cases where D is a prime number. In these cases, the sampling rate conversion cannot be performed in several stages and many of the other existing designs lose their advantages. Special multiplier-free solutions are generated for implementing the filters A/sub k/(z), resulting in dramatic savings. Several examples are included showing the efficiency of the proposed filters compared to other existing designs. >

A novel scheme for implementing a perfect reconstruction filter bank using infinite-impulse-response (IIR) all-pass filters for the processing of infinite length input signals is described. The scheme uses double buffers to implement noncausal, stable synthesis filters operating on infinite length sequences. Finite word-length effects on the performance of the overall system are discussed, and various applications for this structure are proposed. >

An adaptive structure based on a generalised structural subband decomposition of finite-impulse-response (FIR) filters is presented. The proposed structure implements an adaptive FIR filter of length N as a parallel connection of L branches, with each branch composed of a cascade of a fixed interpolator and a sparse adaptive subfilter containing at least N/L non-zero coefficients. The proposed structure presents superior convergence performance for colored input signals when compared to the conventional direct-form least-mean-square (LMS) structure, with a very small increase in the number of operations. The advantages of using the subband structure in the acoustic echo canceller and channel equalizer applications are shown through computer simulation results. >

The concept of overlapped block digital filtering is introduced, and the conditions for shift-invariant operation are derived. Two special types of overlapped block structures which can be used to realized finite impulse response (FIR) filters are discussed. Their efficient implementation based on fast short-length linear convolution algorithms and discrete Fourier transform (DFT) are described. >

Multirate analog-digital systems contain both analog and digital functions on a single integrated circuit and employ different sampling rates at various stages of the system. Both traditional and emerging new applications of such systems are discussed for converting between analog samples and digital words and for realizing processing functions in an easier and more economical way than that would be possible using purely digital or analog techniques. Specific topics addressed include oversampling converters, new conversion architectures based on quadrature-mirror filter (QMF) banks, analog front-end filtering subsystems for video processing, analog-digital multirate systems, and multirate systems for very narrowband bandpass filtering. >

This paper describes a new mixed analog-digital structure suitable for the monolithic implementation of narrowband bandpass filtering and analog-to-digital conversion operations on a single chip. The architecture is based on the combined concepts of N-path filtering and time-interleaved A/D conversion and can be implemented with either predominant digital or mainly analog processing. The comparative advantages of both forms of implementation are discussed from the viewpoints of the ease of integration and robustness against nonideal effects of the required building blocks. Functional simulations performed for a system with 4 MHz center frequency, 150 kHz bandwidth and 12-bit resolution illustrate the operation of the proposed architecture as well as the effects of the main sources of errors.

The classical unsharp masking method of image contrast enhancement is based on the addition of an amplitude scaled linear highpass filtered version of the image to itself. However, the highpass filter also enhances noise components present in the image. Some improvement in the quality of the enhancement has been obtained using a fairly simple quadratic filter in place of the linear highpass filter. The authors first explain why the linear unsharp masking performs well for contrast enhancement of noise free images. A further modification to make the overall approach considerably less sensitive to noise is then proposed. A general class of quadratic filters utilizing Weber's law is also introduced and their important properties are discussed. The modified unsharp masking scheme together with the proposed class of quadratic filters is shown to provide significant improvement in the quality of enhanced images compared to that obtained using similar approaches. >

Proposes a modification to the classic time-frequency permutation method of signal scrambling which reduces its complexity and memory requirements without decreasing its performance. This new approach is applicable to any filter bank or transform and requires only that the decomposition in question be implemented in a polyphase form. To minimize the computational complexity, modulated polyphase filter banks like the cosine-modulated and allpass filter banks can be selected. Using a two dimensional extension to the basic algorithm, the authors consider the problem of image scrambling and include simulation results. >

The generalized frequency domain adaptive filtering (GFDAF) algorithms are efficient implementations of the block least mean square (LMS) algorithm when small block sizes, compared to the number of adaptive coefficients, are required. The behavior of these algorithms is investigated and an examination is made of the use of a self-orthogonalization procedure and of an unconstrained form of the algorithm. Computer simulations are presented verifying the behavior of these methods, and comparing their performance to that of the subband filtering method for the acoustic echo cancelling application. >

The digitally programmable switched-capacitor equalization filter considered uses a structurally allpass section as a basic building block, allowing for orthogonal tuning of center frequency, bandwidth and gain, through the use of three independent capacitor arrays. Effects of finite gain and bandwidth of the operational amplifiers are investigated. Simulation and experimental results are presented verifying the models involved in the analysis. >

Some recently developed unconventional applications of multirate concepts are reviewed, and their usefulness in developing efficient signal processing systems is discussed. The structural subband decomposition of a sequence is described, and some of its applications, such as the efficient design and implementation of FIR (finite impulse response) digital filters, the development of computationally efficient decimators and interpolators, subband adaptive filtering, and the fast computation of discrete transforms are outlined. >

A stochastic analysis is presented of the convergence properties of a second-order adaptive infinite-impulse-response (IIR) notch filter with a gradient-descent coefficient update algorithm. The analysis is based on a linearization of the gradient function in the vicinity of the optimal solution. Expressions for the stability bounds of the algorithm step size and for the steady-state variance of the adaptive parameter are derived. These analytical results are verified by computer simulations for a variety of signal and noise conditions. >

A structure for analog-to-digital (A/D) conversion capable of attaining high resolution and high speed using lower-resolution, lower-speed A/D converters is presented. The structure is based on quadrature mirror filter (QMF) banks, except that the analysis filter bank is a switched-capacitor circuit whereas the synthesis bank is a digital filter circuit. The structure incorporates the advantages of subband coding, and considerably reduces the effect of mismatches among the low-resolution A/D converters. An illustrative example and experimental results verifying the good performance of the proposed approach are included. >

An efficient real-time implementation of digital filtering algorithms using a multiprocessor system in a ring network is investigated. This method is based on a parallel block processing approach, where a continuous supply of input data is divided into blocks and a block is assigned to each processor in rotation. The system is easily expandable and shows a high efficiency even in a large-scale multiprocessing environment. Methods for solving the dependency problems between the processors are also investigated to increase the number of processors which can be used efficiently. Implementation procedures and results for finite impulse response (FIR), recursive, and adaptive filtering algorithms are illustrated. This method has been successfully tested on the SABRINA (Santa Barbara ring network architecture) multiprocessor system developed at the University of California, Santa Barbara, and some experimental results are included. >

A block filter, in general, is a linear, periodic and time-varying (LPTV) system. Under certain conditions satisfied by the transfer function matrix of the filter, the system has an alias free operation, i.e., it behaves like a linear time-invariant (LTI) system. In this paper, we first develop a set of necessary and sufficient conditions for the alias free operation of block filters based on a time-domain analysis of the system. We then develop conditions for the alias free operation of general LPTV systems.

Summary form only given, as follows. Polyphase decomposition of a sequence was advanced to develop computationally efficient interpolators and decimators, and has also been used to design computationally efficient quadrature-mirror filter banks. The polyphase decomposition represents a sequence into a set of sub-sequences, called polyphase components. However, the polyphase components do not exhibit any spectral separation. In this presentation, we first review the concept of structural subband decomposition, generalization of the polyphase decomposition, which decomposes a sequence into a set of sub-sequences with some spectral separation that can be exploited advantageously in many digital signal processing applications. We then outline some of the applications of the structural subband decomposition, such as efficient design and implementation of FIR digital filters, development of computationally efficient decimators and interpolators, subband adaptive filtering, and fast computation of discrete transforms.

Proposes an efficient nonlinear algorithm to suppress impulse noise from highly corrupted images while preserving details and features. The method is applicable to all impulse noise models, including fixed valued (equal height or salt and pepper) impulses and random valued (unequal height) impulses, covering the whole dynamic range. The algorithm is based on a detection-estimation strategy. If a signal sample is detected as a corrupted sample, it is replaced with an estimation of the true value, based on neighborhood information. Otherwise it is kept unchanged. The technique achieves excellent tradeoff between the suppression of noise, and preserving the details and edges without undue increase in computational complexity. Extensive simulation tests indicate that the method performs better than other existing algorithms, including the well known median filters. Illustrative examples included in the paper verify the capability of the proposed approach.

The concept of overlapped block digital filtering is extended to two-dimensional (2D) case. The shift-invariant conditions of 2D overlapped block digital filters are derived. Fast algorithms based on short-length linear convolution algorithms and DFT are then derived. These algorithms are computationally efficient and highly parallel.