In design of Variable Digital Filters (VDFs), Multi-Dimensional (M-D) polynomial approximation is well known as one of the powerful techniques. Although a number of methods for such VDF design can be seen in the literature, nothing has been proposed in this field with emphasis on high-accuracy filter structures with respect to the finite wordlength effects such as coefficient quantization error and roundoff noise. This paper presents M-D polynomial approximation-based VDFs with such a high-accuracy structure. To this end, we first decompose the pre-designed set of constant filters into second-order sections. Then, using the theory proposed in the literature, all of the second-order sections are described in terms of state-space representation of second-order Minimum Roundoff Noise (MRN) structure. Finally the resultant state-space coefficients are approximated by M-D polynomials based on spectral parameters. A numerical example demonstrates that the proposed method simultaneously attains the desired variable characteristics and approximately optimal performances with respect to the finite wordlength effects.

Digital filters based on stochastic computation have recently gained considerable attention because the stochastic computation attains significant reduction of hardware complexity of digital filters compared with the classical deterministic binary computation-based filters. For stochastic IIR filters, Liu and Parhi proposed an elegant method that achieves high precision by means of the normalized state-space lattice structure. This paper extends the result and presents stochastic state-space IIR filters with higher precision than the conventional method. Instead of using the normalized lattice structure, our method makes use of the minimum roundoff noise structure in realizing stochastic state-space filters, leading to further improvement of arithmetic precision of IIR filtering compared with the conventional method. Experimental results show that our method gives higher signal-to-error ratio at the filter outputs than the conventional method.

This paper introduces area/energy-efficient gammatone filters based on stochastic computation. The gammatone filter well expresses the performance of human auditory peripheral mechanism and has a potential of improving advanced speech communications systems, especially hearing assisting devices and noise robust speech-recognition systems. Using stochastic computation, a power-and-area hungry multiplier used in a digital filter is replaced by a simple logic gate, leading to area-efficient hardware. However, a straightforward implementation of the stochastic gammatone filter suffers from significantly low accuracy in computation, which results in a low dynamic range (a ratio of the maximum to minimum magnitude) due to a small value of a filter gain. To improve the computation accuracy, gain-balancing techniques are presented that represent the original gain as the product of multiple larger gains introduced at the second-order sections. In addition, dynamic scaling techniques are proposed that scales up small values only on stochastic domain in order to reduce the number of stochastic bits required while maintaining the computation accuracy. For performance comparisons, the proposed stochastic gammatone filters are designed and evaluated on taiwan semiconductor manufacturing company (TSMC) 65-nm CMOS technology. As a result, the proposed filter achieves an area reduction of 90.7% and an energy reduction of 91.8% in comparison with a fixed-point gammatone filter at the same sampling frequency and a comparable dynamic range.

This paper introduces a design of a gammatone filter based on stochastic computation for area-efficient hardware. The gammatone filter well expresses the performance of human auditory peripheral mechanism and has a potential of improving advanced speech communications systems, especially hearing assisting devices and noise robust speech recognition systems. Using stochastic computation, a power-and-area hungry multiplier used in a digital filter is replaced by a simple logic gate, leading to area-efficient hardware. However, a straightforward implementation of the stochastic gammatone filter suffers from significantly low accuracy in computation, which results in a low dynamic range (a ratio of the maximum to minimum magnitude) due to a small value of a filter gain. To improve the computational accuracy, gain-balancing techniques are presented that represent the original gain as the product of multiple larger gains introduced at the second-order sections. As a result, the proposed techniques maintain the original gain of the filter while improving the computational accuracy. The proposed stochastic gammatone filters are designed and evaluated using MATLAB that achieves a high dynamic range of 71.71 dB compared with a low dynamic range of 5.47 dB in the straightforward implementation.

This paper clarifies the class of second-order digital filters with two second-order modes equal. We consider three cases for second-order digital filters: complex conjugate poles, distinct real poles, and multiple real poles. We derive a general expression of the transfer function of second-order digital filters with two second-order modes equal. Furthermore, we show that the general expression is obtained by a frequency transformation on a first-order prototype FIR digital filter.

This paper proposes a simple method of realization of center frequency adaptive filters for high-accuracy detection of band-pass signals immersed in a broadband signal. Our method extends the conventional method proposed by Kumar and Pal. While the conventional center-frequency adaptive filters were mathematically difficult to describe in the case of high filter order, our method provides a simple procedure to construct any kind of high-order center-frequency adaptive filter. We achieve this goal with the help of the frequency transformation and its block diagram representation. Simulation results show that our high-order center-frequency adaptive filters achieve higher signal-to-noise ratio (SNR) improvement than the conventional low-order filters including the adaptive notch filters.

This paper proposes a motion detection method based on Gaussian mixture model for detecting the moving objects in old film sequences. Conventional motion detection techniques can hardly be applied to the old film sequences due to the influence of intensity flicker. The proposed method combines an adaptive mixture method with a motion detection. The intensities of a particular pixel along the temporal direction are modeled as the Gaussian mixture model. The adaptive mixture method can automatically determine the number of components in the Gaussian mixture model and estimate the parameters of each Gaussian component. Then the components with small weights are chosen as the components corresponding to the moving objects. Experimental results show that the proposed method can effectively detect the moving objects in old film sequences.

This paper proposes variable band-pass/band-stop infinite impulse response (IIR) state-space digital filters with high tuning accuracy and reduced computational complexity. We derive our proposed variable filters from the Gramian-preserving frequency transformation based on the normalized lattice structure of second-order all-pass functions. This approach gives a simple algorithm for control of the frequency characteristics of our proposed variable filters. In addition, we show that our proposed variable filters have smaller number of additions and multiplications than general state-space filters. Furthermore, it is shown that our proposed variable filters have the same controllability/observability Gramians as those of the prototype filters, regardless of the value of the tuning parameter. This property shows the high accuracy of our proposed filters with respect to quantization effects for all tunable frequency characteristics.

This paper proposes analytical synthesis of the minimum L2-sensitivity realizations of all-pass digital filters. We first prove that the L2-sensitivity minimization problem can be solved analytically if the all second-order modes of a digital filter are equal. We focus on the fact that the second-order modes of all-pass digital filters are all unity. As a result, it is clarified that the minimum L2-sensitivity realization of an all-pass digital filter is equal to the balanced realization, which can be synthesized analytically.

This paper presents a new algorithm for realization of Gramian-preserving frequency transformation for linear discrete-time systems. In the proposed algorithm, we construct allpass systems for frequency transformation as the cascaded normalized lattice structure. It is shown that the frequency transformation based on this algorithm not only leaves the controllability/observability Gramians invariant under the change of magnitude responses, but also significantly reduces nonzero entries of the coefficient matrices of transformed systems. This property will be very effective in practical applications such as implementation of high-accuracy multiband state-space digital filters.

This letter presents explicit expressions of the balanced realization of second-order digital filters with real poles. We consider two cases of second-order digital filters: that of real and distinct poles and that of real and multiple poles. Simple formulas are derived for the synthesis of the balanced realizations of these second-order digital filters.

This paper proposes a fast blotch detection algorithm based on a Markov random field (MRF) model with less computational load and with lower false alarm rate than the existing MRF-based algorithms. The proposed algorithm can save the computational time for detecting the blotches by restricting the attention of the detection process only to the candidate areas. The experimental results show that our proposed method provides the computational simplicity and an efficient detecting performance for the blotches.

This paper presents a new analysis of power complementary analog filters using the state-space representation. Our analysis is based on the bounded-real Riccati equations that were developed in the field of control theory. We show that the sum of the controllability/observability Gramians of a pair of power complementary filters is represented by a constant matrix, which is given as a solution to the bounded-real Riccati equations. This result means that power complementary filters possess complementary properties with respect to the Gramians, as well as the magnitude responses of systems. Furthermore, we derive new theorems on a specific family of power complementary filters that are generated by a pair of invertible solutions to the bounded-real Riccati equations. These theorems show some interesting relationships of this family with respect to the Gramians, zeros, and coefficients of systems.

This paper discusses the behavior of the second-order modes of linear continuous-time systems under variable transformations with positive-real functions. We first discuss the case of lossless positive-real transformations, and show that the second-order modes are invariant under any lossless positive-real transformation. We next consider the case of general positive-real transformations, and reveal that the values of the second-order modes are decreased under any general positive-real transformation. We achieve the derivation of these results by describing the controllability/observability Gramians of transformed systems, with the help of the lossless positive-real lemma, the positive-real lemma, and state-space formulation of transformed systems.

This paper proposes a fast convergence algorithm for L2-sensitivity minimization problem of two-dimensional (2-D) separable-denominator state-space digital filters subject to L2-scaling constraints. The proposed algorithm reduces a constrained optimization problem to an unconstrained optimization problem by appropriate variable transformation, and minimizes the L2-sensitivity by iterative calculation called successive substitution method. Our novel algorithm can achieve the L2-sensitivity minimization with quite fast convergence behavior.

The presence of strong acoustic feedback degrades the convergence speed of the active noise control (ANC) filter, and in the worst case the ANC system may become unstable. A fixed feedback neutralization filter, obtained offline, can be used to neutralize the acoustic feedback. The feedback path, however, may be time varying, and we may need continual adjustments during online operation of the ANC system. This paper proposes a new method for online modeling of the acoustic feedback path in ANC systems. The proposed method uses three adaptive filters; a noise control filter, a feedback path modeling (FBPM) filter, and an adaptive noise cancelation (ADNC) filter. The objective of ADNC filter is to remove the disturbance from the desired response of FBPM filter. In comparison with the existing method, which works only for predictable noise sources, the proposed method can work, as well, with the broadband noise sources. The computer simulations are carried out for narrowband (predictable) (case I) and broadband (random) noise sources (case II). It is demonstrated that the proposed method performs better than the existing method in both cases

This paper proposes a new expression of frequency transformation for linear continuous-time state-space systems. The proposed frequency transformation preserves the controllability Gramian and the observability Gramian of prototype state-space systems, and thus allows us to easily realize various kinds of state-space systems keeping the same realization as that of prototype state-space systems. Our result is derived from a modified state-space formulation of frequency transformation and an appropriate state-space representation of reactance functions

This paper proposes a novel approach to L2-sensitivity minimization problem of state-space digital filters subject to L2-scaling constraints. The proposed approach reduces the constrained optimization problem to an unconstrained optimization problem by appropriate variable transformation. As a result, iterative algorithms for the L2-sensitivity minimization without L2-scaling constraints can be applied to the L2-sensitivity minimization subject to L2-scaling constraints. Our novel approach can achieve the L2-sensitivity minimization with quite faster convergence behavior

This paper proposes a closed form solution to L2-sensitivity minimization of second-order state-space digital filters. Restricting ourselves to the 2nd order case of state-space digital filters, we can formulate L2-sensitivity minimization problem by hyperbolic functions. As a result, L2-sensitivity minimization problem can be converted into a problem to find the solution to a 4th degree polynomial equation of constant coefficients, which can be algebraically solved in closed form without iterative calculations

This paper proposes a new method for online secondary path modeling in active noise control systems. The existing methods for active noise control systems with online secondary path modeling consist of three adaptive filters. The main feature of the proposed method is that it uses only two adaptive filters. In the proposed method, the modified-FxLMS (MFxLMS) algorithm is used in adapting the noise control filter and a new variable step size (VSS) least mean square (LMS) algorithm is proposed for adaptation of the secondary path modeling filter. This VSS LMS algorithm is different from the normalized-LMS (NLMS) algorithm, where the step size is varied in accordance with the power of the reference signal. Here, on the other hand, the step size is varied in accordance with the power of the disturbance signal in the desired response of the modeling filter. The basic idea of the proposed VSS algorithm stems from the fact that the disturbance signal in the desired response of the modeling filter is decreasing in nature, (ideally) converging to zero. Hence, a small step size is used initially and later its value is increased accordingly. The disturbance signal, however, is not available directly, and we propose an indirect method to track its variations. Computer simulations show that the proposed method gives better performance than the existing methods. This improved performance is achieved at the cost of a slightly increased computational complexity.

This paper proposes a new structure for feedforward active noise control (ANC) systems with online secondary path modeling. The proposed method: 1) uses the same error signal for updating the noise control process as used for the secondary path modeling process and 2) incorporates an adaptive filtering with averaging based filtered-reference algorithm in the noise control process. The computer simulations have been conducted with both narrowband and broadband noise signals. It is shown that in the proposed ANC system the residual noise signal and the secondary-path-modeling error can be reduced at a faster convergence rate than the existing methods. This improved performance is achieved at the expense of a slightly increased computational complexity.

This letter proposes an adaptive filtering with averaging-based algorithm for active noise control (ANC) systems. This algorithm uses a similar structure as that of the FxLMS-based ANC system. The proposed algorithm, called Filtered-x Adaptive Filtering with Averaging (FxAFA) algorithm, uses averages of both data and correction terms to find the updated values of the tap weights of the ANC controller. The computer simulations are conducted for single-channel feedforward ANC systems. It is shown that the proposed algorithm gives fast convergence as compared with the FxLMS algorithm and achieves better performance in the presence of the measurement noise. The comparison with the FxRLS algorithm shows that the proposed FxAFA algorithm is a better choice for low computational complexity and stable performance.

This letter proposes frequency transformation for two-dimensional (2-D) digital filters in terms of the state-space equations. In order to derive the 2-D state-space formulation of the frequency transformation, we extend Mullis and Roberts' state-space formulation of one-dimensional frequency transformation to 2-D case. The proposed frequency transformation is very suitable for state-space analysis of the transformed filters since the resultant formulation consists of simple algebraic operations such as matrix addition, multiplication, inverse and so on. It can be easily implemented in MATLAB without any complicated algorithm.

This paper proposes a synthesis method for low coefficient sensitivity second-order IIR digital filter structures using Genetic Programming with Automatically Defined Functions (GP-ADF). In this paper, digital filter structures are represented as S-expressions with subroutines. It is easy to generate syntactically valid S-expressions and perform the genetic operations because the representation is suitable for GP. In a numerical example, we use the fitness measure including the magnitude sensitivity, and demonstrate that the proposed method can synthesize efficiently very low coefficient sensitivity filter structures.

This letter proposes a synthesis method for low coefficient sensitivity second-order IIR digital filter structures using genetic programming with automatically defined functions (GP-ADF). In this letter, digital filter structures are represented as S-expressions with subroutines. It is easy to generate syntactically valid S-expressions and perform the genetic operations, because the representation is suitable for GP. A numerical example uses the fitness measure, including the magnitude sensitivity, and demonstrates that the proposed method can synthesize efficiently very low coefficient sensitivity filter structures.

This paper proposes a moment based encoding algorithm for iterated function system (IFS) coding of nonhomogeneous fractal images with unequal probabilities. Moment based encoding algorithms for IFS coding of non-homogeneous fractal images require a solution of simultaneous algebraic equations that are difficult to handle with numerical root-finding methods. The proposed algorithm employs a variable elimination method using Grobner bases with floating-point coefficients in order to derive a numerically solvable equation with a single unknown. The algorithm also employs a varying associated-probabilities method for the purpose of decreasing the computational complexity of calculating Grobner bases. An experimental result shows that the computational time for encoding the non-homogeneous fractal image "Curl" of 256/spl times/256 pixels and 256 gray levels is 207 seconds on a PC with a 233 MHz Pentium II processor.

This paper presents a GA-based design method for multiplierless 2-D state-space digital filters (SSDFs) with very small roundoff noise. All coefficients of the designed 2-D SSDFs are expressed as the sum of two powers-of-two terms. Consequently, the multiplierless 2-D SSDFs are attractive for the high-speed operation and simplification of hardware, since the signal in the filters can be processed by fewer shifting operations and additions instead of multiplications. The proposed method can design multiplierless 2-D SSDFs without significantly increasing the roundoff noise power gain and with smaller approximation error than those of the other methods which use transfer functions in a continuous coefficient space. The effectiveness of the proposed method is demonstrated with a design example.

This paper presents a new design method of 2-D state-space digital filters (2D-SSDFs) with powers-of-two coefficients based on a genetic algorithm (GA). The design problem is formulated in a state-space model. All coefficients of 2D-SSDF are then encoded to binary strings in order to apply the GA to the design problem. In addition, a stability test routine is embedded in the GA procedure to ensure the stability of the resulting 2D-SSDFs. The proposed method can obtain 2D-SSDFs with small approximation error in a nonuniform discrete space such as powers-of-two coefficients, which means that the designed 2D-SSDFs are attractive for high-speed operation and simple hardware architecture. The effectiveness of the proposed method is demonstrated by a design example.

The paper proposes an optimal design method of separable-denominator (SD) two-dimensional digital filters (2DDFs) based on a simple genetic algorithm (SGA) for frequency-domain specifications. Parameters of the transfer function of a SD-2DDF are encoded to bit strings in order to apply a SGA to the design. Stability of a 2DDF is easily checked because of the separability of the denominator of the transfer function. The proposed method has flexibility for change of specifications of 2DDFs, and enables one to use arbitrary error functions. The usefulness of the proposed method is demonstrated by design examples.>

Iterated transformation theory-based coding (ITTBC) suffers from very high computational complexity in the encoding phase. This is due to its exhaustive search. This paper proposes a multiresolution tree search ITTBC (MTS-ITTBC) to reduce the encoding complexity. MTS-ITTBC searches the ITT-code using a multiresolution search-tree. The computational load of MTS-ITTBC is O(NlogN), while that of full search ITTBC is O(N/sup 2/), where N is the number of range blocks or domain blocks in an image. Numerical examples show that the encoding time of MTS-ITTBC can be reduced to 14% of that of the full search ITTBC, while the loss in quality relative to the full search ITTBC is about 0.5 dB in p-pSNR, which is visually negligible.>

This paper proposes a newly defined sensitivity called a statistical sensitivity. The statistical sensitivity is minimized, and minimum sensitivity structures are obtained via equivalent transformations. The sensitivity of linear systems can be interpreted by the controllability and observability concepts of the state-space.

This paper studies the roundoff noise and the scaling in 2-D state space digital filters. The noise matrix and the covariance matirx in the 2-D case are derived. They are expressed with infinite sum or double integral. A formulation is given to synthesize minimum roundoff noise 2-D state space digital filters. A numerical example is given to show the methods of analysis and synthesis.

This paper proposes a unified design method of state-space digital filters using system balancing concept. This method is formed by applying a newly discovered relation between the balanced realizations and the optimal realizations of digital filters to the approximation method that results in balanced realizations. It can perform the approximation and the synthesis problems of the filter design simultaneously and efficiently, and can yield suboptimal digital filters which approximate given impulse responses closely and suppress limit cycles.

Arbitrary digital filters are uniquely described by the element equations proposed here in which the outputs of adders and multipliers are defined as variables in addition to state variables. Equations of overflow oscillations in arbitrary digital filters are represented using the simultaneous equations or the DFT. A sufficient condition for absence of overflow oscillations is obtained by means of the element equations and the second method of Liapunov, and is applied to a ladder form as an example.