The complexity of Finite Impulse Response (FIR) filters is mainly dominated by the number of adders (subtractors) used to implement the coefficient multipliers. It is well known that Common Subexpression Elimination (CSE) method based on Canonic Signed Digit (CSD) representation considerably reduces the number of adders in coefficient multipliers. Recently, a binary-based CSE (BSE) technique was proposed, which produced better reduction of adders compared to the CSD-based CSE. In this paper, we propose a new 4-bit binary representation-based CSE (BCSE-4) method which employs 4-bit Common Subexpressions (CSs) for implementing higher order low-power FIR filters. The proposed BCSE-4 offers better reduction of adders by eliminating the redundant 4-bit CSs that exist in the binary representation of filter coefficients. The reduction of adders is achieved with a small increase in critical path length of filter coefficient multipliers. Design examples show that our BCSE-4 gives an average power consumption reduction of 5.2% and 6.1% over the best known CSE method (BSE, NR-SCSE) respectively, when synthesized with TSMC-0.18 µm technology. We show that our BCSE-4 offers an overall adder reduction of 6.5% compared to BSE without any increase in critical path length of filter coefficient multipliers.

In this comment we point out that the mapping from carry-propagation adders to carry-save adders in the context of shift-and-add multiplication is inconsistent. Based on this it is shown that the implementation in Ref.[1] does not achieve any complexity reduction in practice.

An explicit expression for the impulse response coefficients of the predictive FIR digital filters is derived. The formula specifies a four-parameter family of smoothing FIR digital filters containing the Savitsky-Goaly filters, the Heinonen-Neuvo polynomial predictors, and the smoothing differentiators of arbitrary integer orders. The Hahn polynomials, which are orthogonal with respect to a discrete variable, are the main tool employed in the derivation of the formula. A recursive formula for the computation of the transfer function of the filters, which is the z-transform of a terminated sequence of polynomial ordinates, is also introduced. The formula can be used to design structures with low computational complexity for filters of any order.

Using a pair of matched square-root-raised-cosine (SRRC) filters in the transmitter and the receiver in a band-limited digital communication system can theoretically achieve zero inter-symbol interference (ISI). In reality, the ISI cannot be zero when both SRRC filters are approximately implemented because of some numerical precision problems in the design phase as well as in the implementation phase. In this paper, the author proposes an iterative method to design the coefficients of SRRC FIR filters. The required ISI of the system can be specified such that both ISI and frequency domain specifications are monitored in the design phase. Since the ISI can be specified beforehand, the tradeoff between performance and the filter length becomes possible in the proposed design algorithm.

R-regular Mth band filters are an important class of digital filters and are used in constructing Mth-band wavelet filter banks, where the regularity is essential. But this kind of filter has larger stopband peak errors compared with a minimax filter of the same length. In this paper, peak errors in stopband of R-regular 4th-band filters are reduced by means of superimposing two filters with successive regularities. Then the stopband peak errors in the resulting filters are compared with the original ones. The results show that the stopband peak errors are reduced significantly in the synthesized filter that has the same length as the longer one of the two original filters, at the cost of regularity.

In this paper, we present a new numerical method for the complex approximation of FIR digital filters. Our objective is to design FIR filters with equiripple magnitude and phase errors. The proposed method solves the least squares (LS) problem iteratively. At each iteration, the desired response is updated so as to have an equiripple error. The proposed methods do not require any time-consuming optimization procedure such as the quasi-Newton methods and converge to equiripple solutions quickly. We show some examples to illustrate the advantages of our proposed methods.

A finite impulse response (FIR) core based on the cascoded class AB SI technique is presented for low power wireless transceivers. Accomplished through both architectural and circuit developments, the filter's features include high speed, low power consumption, small silicon area and compatibility with standard CMOS process. For feasibility and performance assessments, an 8-tap 16 MS/s SI FIR filter with 5-bit coefficients and a 31-tap 80 MS/s SI matched filter (MF) for despreading task in future WCDMA receivers are demonstrated via simulations.

This paper presents a Field-Programmable Digital Filter (FPDF) IC that employs carry-propagation-free redundant arithmetic algorithms for faster computation and multiple-valued current-mode circuit technology for high-density low-power implementation. The original contribution of this paper is to evaluate, through actual chip fabrication, the potential impact of multiple-valued current-mode circuit technology on the reduction of hardware complexity required for DSP-oriented programmable ICs. The prototype FPDF fabrication with 0.6 µm CMOS technology demonstrates that the chip area and power consumption can be reduced to 41% and 71%, respectively, compared with the standard binary logic implementation.

This article presents a three-step method for designing linear phase FIR filters with signed-powers-of-two (SPT) coefficients. In Step one, a prototype optimal FIR filter is designed by the Remez exchange algorithm. In Step two, a scaling factor is selected by employing simple ad-hoc rules. In Step three, each coefficient of the prototype filter is scaled by the scaling factor and is quantized coarsely as the canonic-signed-digit (CSD) representation. Then, a mixed-integer-linear-programming (MILP) algorithm is applied to three least significant digits (LSDs) of the filter's coefficients to reduce the number of SPT terms. Design examples demonstrate that the proposed algorithm is able to produce linear phase fixed-point FIR filters using fewer SPT terms than the existing methods under the same normalized peak ripple magnitude (NPRM) specification.

Time series prediction is very important technology in a wide variety of fields. The actual time series contains both linear and nonlinear properties. The amplitude of the time series to be predicted is usually continuous value. For these reasons, we combine nonlinear and linear predictors in a cascade form. The nonlinear prediction problem is reduced to a pattern classification. A set of the past samples x(n-1),. . . ,x(n-N) is transformed into the output, which is the prediction of the next coming sample x(n). So, we employ a multi-layer neural network with a sigmoidal hidden layer and a single linear output neuron for the nonlinear prediction. It is called a Nonlinear Sub-Predictor (NSP). The NSP is trained by the supervised learning algorithm using the sample x(n) as a target. However, it is rather difficult to generate the continuous amplitude and to predict linear property. So, we employ a linear predictor after the NSP. An FIR filter is used for this purpose, which is called a Linear Sub-Predictor (LSP). The LSP is trained by the supervised learning algorithm using also x(n) as a target. In order to estimate the minimum size of the proposed predictor, we analyze the nonlinearity of the time series of interest. The prediction is equal to mapping a set of past samples to the next coming sample. The multi-layer neural network is good for this kind of pattern mapping. Still, difficult mappings may exist when several sets of very similar patterns are mapped onto very different samples. The degree of difficulty of the mapping is closely related to the nonlinearity. The necessary number of the past samples used for prediction is determined by this nonlinearity. The difficult mapping requires a large number of the past samples. Computer simulations using the sunspot data and the artificially generated discrete amplitude data have demonstrated the efficiency of the proposed predictor and the nonlinearity analysis.

This paper compares signal classification performance of multilayer neural networks (MLNNs) and linear filters (LFs). The MLNNs are useful for arbitrary waveform signal classification. On the other hand, LFS are useful for the signals, which are specified with frequency components. In this paper, both methods are compared based on frequency selective performance. The signals to be classified contain several frequency components. Furthermore, effects of the number of the signal samples are investigated. In this case, the frequency information may be lost to some extent. This makes the classification problems difficult. From practical viewpoint, computational complexity is also limited to the same level in both methods.IIR and FIR filters are compared. FIR filters with a direct form can save computations, which is independent of the filter order. IIR filters, on the other hand, cannot provide good signal classification deu to their phase distortion, and require a large amount of computations due to their recursive structure. When the number of the input samples is strictly limited, the signal vectors are widely distributed in the multi-dimensional signal space. In this case, signal classification by the LF method cannot provide a good performance. Because, they are designed to extract the frequency components. On the other hand, the MLNN method can form class regions in the signal vector space with high degree of freedom.

The ringing occurred in the step response causes an undesirable stripe pattern in TV signals. A simultaneous approximation with both the frequency and the step response is required in the designing filter which is used in the image signal processing in order to prevent the ringing. The wellknown Remez algorithm for designing FIR filters approximates the response only in the frequency domain. As the result, the filters designed by this algorithm causes the large ringing in the step response. In this paper, we propose the method of design for FIR filters with minimum amplitude in the stopband, under the condition that the step response has no ringing and the prescribed rise characteristics. For this end, we use the constrained successive projections method.

In this paper,novel techniques for designing Finite Impulse Response (FIR) digital integrators have been given. The design is based on analytical approach for computing the weights required in the structures. Exact mathematical formulas for computing these weights have been derived.

In multidimensional signal sampling, the orthogonal sampling scheme is the simplest one and is employed in various applications, while a non-orthogonal sampling scheme is its alternative candidate. The latter sampling scheme is used mainly in application where the reduction of the sampling rate is important. In three-dimensional (3-D) signal processing, there are two typical sampling schemes which belong to the non-orthogonal samplings; one is face-centered cubic sampling (FCCS) and the other is body-centered cubic sampling (BCCS). This paper proposes a new design method for 3-D band-limiting FIR filters required for such non-orthogonal sampling schemes. The proposed method employs the McClellan transformation technique. Unlike the usual 3-D McClellan transformation, however, the proposed design method uses 2-D prototype filters and 2-D transformation filters to obtain 3-D FIR filters. First, 3-D general sampling theory is discussed and the two types of typical non-orthogonal sampling schemes, FCCS and BCCS, are explained. Then, the proposed design method of 3-D bandlimiting filters for these sampling schemes is explained and an effective implementation of the designed filters is discussed briefly. Finally, design examples are given and the proposed method is compared with other method to show the effectiveness of our methos.

This paper proposes a new design method of variable FIR digital filters. The method uses a multi-dimensional linearphase FIR filter as a prototype. The principle of the proposed method is based on the fact that the crosssectional characteristics of a 2-D filter along with a line vary if the intersection of this line is changed. The filter characteristics can be varied by recalculating all the filter coefficients from proposed equations, which leads to an advantage that the variable range is very wide. Another advantage is that the passband and stopband deviations are completely predetermined in the design procedures and that the passband edge can be accurately settled to a desired frequency while keeping the transition band width unchanged. First the proposed design method is explained and the effect of the transition band of 2-D filters is discussed. Then the calculation cost required in updating the filter coefficients are considered. Finally two design examples are presented and the proposed method is compared with the existing one, which shows the usefulness of our method.