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The main objective of this paper is to design and implement minimum multiplier, low latency structures of a comb filter. Multipliers are the most area and power consuming elements; therefore, it is desirable to realize a filter with minimum number of multipliers. In this paper, design of comb filters based on lattice wave digital filters (LWDF) structure is proposed to minimize the number of multipliers. The fundamental processing unit employed in LWDF requires only one multiplier. These lattice wave digital comb filters (LWDCFs) are realized using Richards' and transformed first-order and second-order all-pass sections. The resulting structural realizations of LWDCFs exhibit properties such as low coefficient sensitivity, high dynamic range, high overflow level, and low round-off noise. Multiplier coefficients of the proposed structures are implemented with canonic signed digit code (CSDC) technique using shift and add operations leading to multiplierless implementation. This contributes in reduction of number of addition levels which reduces the latency of the critical loop. A field programmable gate array (FPGA) platform is used for evaluation and testing of the proposed LWDCFs to acquire advantages of the parallelism, low cost, and low power consumption. The implementation of the proposed LWDCFs is accomplished on Xilinx Spartan-6 and Virtex-6 FPGA devices. By means of examples, it is shown that the implementations of the proposed LWDCFs attain high maximum sampling frequency, reduced hardware, and low power dissipation compared with the existing comb filter structures. Copyright © 2017 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

One-bit signal processing based on delta-sigma modulation has been studied for hardware implementation of signal processing systems. In the 1-bit signal processing, finite word-length problems such as overflow and coefficient quantization error occur. To solve the problems, a new design method with state space is proposed in this paper. Digital filters are designed to show the feasibility of the method. First, the L/ L-sensitivity is shown to evaluate coefficient quantization error and L scaling constraints to prevent overflow. Second, a state space equation is presented and the L/ L-sensitivity and L-scaling constraints are extended to take the filter structure and oversampling effects into account. Finally, the proposed method is shown to attain a higher SNR than conventional ones. © 2011 Wiley Periodicals, Inc. Electr Eng Jpn, 175(4): 48-56, 2011; Published online in Wiley Online Library (). DOI 10.1002/eej.21075 [ABSTRACT FROM AUTHOR]

In the hardware implementation of FIR (Finite Impulse Response) digital filters, it is desirable to reduce the total number of nonzero digits used for representation of the filter coefficients. In general, the design problem of FIR filters with CSD (Canonical Signed Digit) representation, which is efficient for reduction of the number of multiplier units, is often treated as a 0-1 combinational problem. In such problems, certain difficult constraints hinder linearization of the problem. Although many kinds of heuristic approaches have been used to solve the problem, the solutions obtained in such a manner cannot be guaranteed to be optimal. In this paper, we attempt to formulate the design problem as a 0-1 mixed integer linear programming problem and to solve it by using the branch and bound technique, which is a powerful method for solving integer programming problems. Several design examples are presented to illustrate the efficient performance of the proposed method. © 2011 Wiley Periodicals, Inc. Electron Comm Jpn, 94(6): 10-16, 2011; Published online in Wiley Online Library (). DOI 10.1002/ecj.10331 [ABSTRACT FROM AUTHOR]

An optimal design method for stable IIR (Infinite Impulse Response) filters under the min-max criterion is proposed. The design problem considered is the complex Chebyshev approximation of a rational function including the stability constraint. We formulate this problem as a problem of real linear semi-infinite programming problem using the real rotation theorem. The problem is solved by the three-phase method; one of the methods is used for solving semi-infinite programming problems. The three-phase method includes three operations. In the first operation, some active constraint candidates are selected by the iterative simplex method. Next, the second operation integrates some degenerate constraints. In the third operation, the approximate solution obtained up to the second operation is adjusted so as to satisfy the optimality condition. The filters designed by the method are found to be more precise than those designed by the conventional method. Several design examples are presented to demonstrate the effectiveness of the proposed method. © 2011 Wiley Periodicals, Inc. Electron Comm Jpn, 94(6): 17-23, 2011; Published online in Wiley Online Library (). DOI 10.1002/ecj.10330 [ABSTRACT FROM AUTHOR]

In this article, we propose and design bandstop filters with capacitive coupled-line structure. The coupled-line structure has small area, wide bandwidth, and steep insertion loss response. In simulation, we used Serenade and Sonnet EM simulation tools to analyze the characteristics of filters. In circuit implementation, we selected FR-4 substrates. We used coupled-lines on capacitive coupling bandstop filters to reduce the size about 58% and to create two attenuated poles for increasing bandwidth. First we derived the relation between the odd-mode and even-mode impedance theoretically. Then, we applied EM software tools to choose a proper coupling distance to implement circuit layout. Finally, the measured results were compared with the simulated results, and we found that coupled-lines can effectively improve the reduction size of the filters. © 2008 Wiley Periodicals, Inc. Microwave Opt Technol Lett 50: 1363–1368, 2008; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.23374 [ABSTRACT FROM AUTHOR]

Digital filters with a linear phase characteristic are needed in many applications for signal processing. In this paper, design of a Chebyshev-type IIR filter with approximate linear phase characteristics in the passband is described. First, it is shown that a flat stopband can easily be realized by placing multiple zeros at the specified frequency points in the stopband. Next, the complex Remez exchange algorithm is applied to the passband so that the filter design problem is formulated as an eigenvalue problem. Hence, by solving the eigenvalue problem, the filter coefficients can be derived easily. Further, by means of iterative calculations, an equiripple characteristic of the error function in the passband is obtained. Finally, it is shown that a reverse Chebyshev-type IIR filter with an approximate linear phase characteristic can also be obtained by parallel connection of the proposed Chebyshev-type filter and a delay line. © 2003 Wiley Periodicals, Inc. Electron Comm Jpn Pt 3, 87(2): 1–9, 2004; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ecjc.10133 [ABSTRACT FROM AUTHOR]

It is known that linear phase FIR digital filters fall into four types considering the symmetry of impulse response. For example, filters of type 2 can be used at the time of partitioning and reconstruction of signals in multirate signal processing, and other types have similar special applications. Moreover, the linear phase FIR digital filters with flat passband and equiripple stopband characteristics are very important filters in practice because they have better time domain characteristics and less ringing than Chebyshev filters with equiripple stopband and passband characteristics. However, conventional design methods are restricted to type 1. In this paper, we therefore propose a method of design of linear phase FIR digital filters with flat passband and equiripple stopband characteristics for all four types. The proposed function is composed of two functions, one with a flat characteristic in the passband and the second with equiripple characteristics in the stopband. The latter function is obtained by using the well-known Remez algorithm only for the stopband. © 2002 Wiley Periodicals, Inc. Electron Comm Jpn Pt 3, 86(4): 89–95, 2003; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ecjc.1148 [ABSTRACT FROM AUTHOR]

In general, signals with 90° phase difference from an orthogonal phase oscillator or a phase difference detector are used for measurement of the frequency characteristics of a complex coefficient filter with two input terminals for the real part and the imaginary part. However, since the phase splitter is designed by an approximate method, the phase difference of its output signal has an error. This paper describes the effect of the phase difference of the input signal on the error in the measurement of the frequency characteristics of a complex coefficient filter. Next, two new methods are described for deriving the frequency response of the complex coefficient filter without using an orthogonal phase oscillator or a phase splitter. The proposed method can be realized by providing the in-phase and out-of-phase signals to two input terminals or by providing the signal only to one of the terminals while the other is grounded. Finally, the frequency response of the complex coefficient filter is measured with the proposed method and its effectiveness is confirmed. © 2002 Scripta Technica, Electron Comm Jpn Pt 3, 85(6): 32–41, 2002 [ABSTRACT FROM AUTHOR]

A nonuniform filter bank divides the band nonuniformly according to the properties of the signal, which is expected to be more effective than a uniform division filter bank in applications such as subband coding. The structure of the nonuniform filter bank, however, is complex. In particular, no investigation has been made of the linear-phase nonuniform filter bank. From such a viewpoint, this paper considers a perfect reconstruction nonuniform filter bank with linear phase, and derives the necessary and sufficient conditions for a perfect reconstruction system as well as for a linear-phase filter. Then, a design method is presented based on the amplitude distortion in the frequency domain and the elimination of aliasing. By the proposed method, the nonuniform filter bank can be designed directly without using the equivalent transformation to the uniform filter bank. © 2000 Scripta Technica, Electron Comm Jpn Pt 3, 83(8): 103–114, 2000 [ABSTRACT FROM AUTHOR]

With the advent of the radio relay system and multilevel modulation, the multicarrier system and variable capacity transmission system are proposed to realize excellent performance in the lading channel. Accordingly. ills desired to realize & highly functional MODEM which can cope with those systems in a flexible way. On the other hand, intensive studies have been made on digital signal processing in the modulation and demodulation in the field of data modem. However, these methods consider the low-rate system of 1ess than 100 Kbaud and are difficult to apply directly to the system where the transmission rate of 10 Mbaud or above is required For the foregoing masons, this paper considers the realization of the all-digital modulator which can realize the high-capacity transmission of over 10 Mbaud for the multilevel modulation system, such as 256 QAM. This paper discusses the design of the digital filter with excellent intersymbol interference. The condition for the carrier frequency for a given clock rate is presented. Then a variable multilevel modulator with a simple correction circuit is proposed which can be applied to the variable-capacity transmission system. Finally, the proposal circuit is constructed and it is confirmed that an excellent modulation performance is obtained without adjustment in various multilevel modulation systems. [ABSTRACT FROM AUTHOR]

The multirate digital filter is useful in realizing narrowband characteristics because multiplication can be reduced by using different sampling frequencies, at the same time reducing the order of the filter to be realized. This paper introduces the complex coefficient into the traditional design of the low-pass multirate filter. The construction method is proposed for the multirate bandpass digital filter with complex coefficients. By applying the complex coefficient filters to the decimeter and interpolator composing the multirate filter, bandpass characteristics can easily be obtained. By employing the multistage cascade structure, the number of multiplications and the memory capacity for coefficients can be reduced greatly. Then a new design method for the complex-coefficient filter is proposed based on the properties of the analytic signal. The discussion in this paper applies to both FIR and IIR filters. [ABSTRACT FROM AUTHOR]

In designing a two-dimensional digital filter with special consideration of the phase characteristics, particularly the group delay characteristics, a very high-order filter is generally required. This paper extends the coefficients of the filter from real to complex and describes a design technique for comparatively low-order, two-dimensional, circularly symmetric filters with consideration of phase characteristics. First, the method of transforming a two-dimensional input signal into an analytic signal is described and then the design technique of two kinds of complex coefficient filters which use the properties of analytic signals is discussed. In the first kind variable transformation to a 1-D real coefficient FIR filter is used to obtain a 2-D has the merits of permitting independent setting of the sharpness of cutoff characteristics and circular symmetry. In the other kind of complex coefficient filter a recursive digital filter is obtained by using an all-pole filter having constant group delay in the passband of the transfer function and having a 2-D complex coefficient mirror image polynomial. It always then values of the coefficients and the overall group delay is also constants. Moreover, in this paper, design examples based on these methods are given and the validity of our methods is shown. [ABSTRACT FROM AUTHOR]

In the field of one-dimensional signal processing, the concept of analytic signal has been introduced in order to yield a low-pass expression for band-pass-type signals. This analytic signal is obtained by adding the Hilbert transform of the real numbers as the imaginary part to the original signal. One important property of this signal is that its Fourier transform vanishes for negative frequencies, i.e., it "appears only in the positive frequency axis." This property is applied to the design of one-dimensional digital filters. In this paper, a signal processing algorithm using two-dimensional digital filters with complex coefficients is proposed. This is done by extending the concept of analytic signal to two dimensions; the processing uses the fact that its Fourier Transform "exists only in the right half-plane of the two-dimension frequencies plane" or, in the case of quadrantal symmetry, "only in the first quadrant of the two-dimension frequencies plant." Using this algorithm, the degree of freedom for the design of 2D filters is increased and closed design methods for circularly symmetric filters and various new fan filters are possible. Moreover, difficulties of presently known methods such as high-order requirements and limitations upon the cutoff frequency are greatly relaxed. [ABSTRACT FROM AUTHOR]

In digital beamforming (DBF) antennas, received propagation signals are first converted down into baseband inphase and quadrature signals, then DBF signal processing is done. We propose a method for designing two-dimensional (2D) digital filters utilized in such DBF networks to handle the signals with wide fractional bandwidths up to 40%. First, we consider the relationship between DBF and its 2D normalized frequency description. Here, we show that 2D complex coefficient digital filters with nonsymmetric characteristics are necessary to form broadband beams. Next, based on this consideration, we describe the proposed method, which combines spectral transformation and a window method. Note that approximation is achieved such that the beam pattern, including its sidelobe characteristics, from the resulting broadband DBF network is virtually frequency-independent. As a result, it has become possible to design DBF networks suitable for a multibeamforming network for use in the broadband beamspace adaptive array antenna proposed in Sekiguchi, Miura, and Karasawa [9]. © 1998 Scripta Technica. Electron Comm Jpn Pt 3, 81(3): 22–34, 1998 [ABSTRACT FROM AUTHOR]

In this paper, we propose a design method of perfect reconstruction (PR) nonuniform filter banks. Filter banks are roughly separated into nonparaunitary and paraunitary ones. Paraunitary filter banks have some advantages: for example, the frequency responses of synthesis filters are identical to those of analysis filters. However, the severe constraint makes it difficult to design them and, especially in the nonuniform case, the design method becomes complex for some frequency-division cases. Thus, we concentrate on nonparaunitary filter banks and present a design method for nonuniform filter banks with arbitrary lengths and frequency divisions. © 1997 Scripta Technica, Inc. Electron Comm Jpn Pt 3, 80(10): 51–59 1997 [ABSTRACT FROM AUTHOR]

This paper describes an efficient structure for generalized lapped orthogonal transforms (GenLOT) for finite-duration sequences, which we expect to be used for subband image coding. When linear convolution is carried out on the finite-duration sequences and filter, the number of points in the output signal increases. Therefore, the linear convolution is not desirable in subband image coding. In order to solve this problem, the convolution is carried out after the finite-duration sequences are symmetrically and periodically extended (symmetric extension method). This method is superior to circular convolution because the former method causes less distortion at the signal boundaries. In the GenLOT structure proposed in this paper, the symmetric extension can be realized without redundant operations due to signal extension and, furthermore, with fast implementation. This structure is considered to be a generalization of the lapped orthogonal transform (LOT) for finite-duration sequences. In addition, its application to the M-band discrete-time wavelet transform (DTWT) will be described. Finally, it will be shown that an efficient structure for finite-duration sequences can be realized in the M-band DTWT. © 1997 Scripta Technica, Inc. Electron Comm Jpn Pt 3, 80(10): 39–50, 1997 [ABSTRACT FROM AUTHOR]

There are some applications that require oversampled filter banks, for example, adaptive signal processing using multirate filter banks. Little study was done, however, for such filter banks compared with maximally decimated ones. In this paper, we propose a design method for oversampled filter banks which satisfy the perfect reconstruction and linear phase properties. Moreover, we consider the design method for both orthogonal and biorthogonal ones. When the decimation ratio is not a divisor of the number of channels, we find it impossible for analysis and synthesis filters to have the same frequency responses by considering the mechanism of aliasing cancellation. In other words, biorthogonal filter banks can be designed under an arbitrary decimation ratio, while it is restricted to a divisor of the number of channels in the orthogonal case. We first derive the conditions for perfect reconstruction and linear phase for both biorthogonal and orthogonal ones. Then, we present the design method for both cases. Finally, some design examples are shown. © 1997 Scripta Technica, Inc. Electron Comm Jpn Pt 3, 80(10): 78–86, 1997 [ABSTRACT FROM AUTHOR]

This paper proposes the parallel construction of the second-order infinite impulse response (IIR) adaptive digital filter (ADF) as an adaptive digital filter for eliminating multiple narrowband signals mixed in the broadband signal. Then the pole-control method for the filter is proposed. In the proposed pole-control, the pole radius and the pole argument are controlled separately by different algorithms. In this study, the pole argument is corrected by estimating the deviation of the central frequency of the signal to be eliminated from the convergent value of the multiplier coefficient that determines the zero. The pole radius is controlled by the method that determines the direction of correction, using the parallel-connected three ADFs with the same pole argument and a slightly different pole radius. It is verified by a simulation that those pole-control methods work effectively. It is demonstrated that the pole radius and the pole argument can be controlled simultaneously. [ABSTRACT FROM AUTHOR]

The unifying treatment of a general gradient adaptive algorithm studied here is based on the principles of minimum mean square method and instrumental variable method by formulating the general oblique projection algorithm, including finite impulse response (FIR) and serial-parallel infinite impulse response (IIR)-type configurations. The oblique projection algorithm of low-order past-value data space is derived in which the dimension of past-due data space can be easily adjusted, including the least mean square (LMS) method, learning-identification method and gradient instrumental variable method (GIVE). Next, the new analysis model which describes the convergence process of general gradient algorithm is shown and the convergence conditions are indicated for the first and second moment with arbitrary inputs. It is found that this condition is more severed as compared with the white input. Moreover, the process of convergence of these conditions is studied by simulation. [ABSTRACT FROM AUTHOR]

Two-dimensional (2-D) diamond-shaped filters are important filters with many applications and are known to be designed and implemented efficiently as 2-D half- band filters. On the other hand, filters with different number of taps in both directions are often suitable for a specific application rather than filters with equal number of taps. This paper proposes a design method for 2-D maximally flat diamond-shaped filters with rectangular support of impulse response. First, the maximally flat conditions at the origin are considered together with equations which make the filter approximately diamond-shaped. Then, by combining the derived conditions to form a system of linear equations with respect to the independent filter coefficients, designs for the difference in the number of taps 2, 4, and 6 are demonstrated. Finally, together with giving several design examples, comparison with other design methods are made and the usefulness of the suggested design method is verified. [ABSTRACT FROM AUTHOR]

The filter on monolithic LSI for communication and measurement is realized by the digital signal processor (DSP) or the switched capacitor (SC) circuit. In the analog-digital interface, high-speed processing, applications requiring low power consumption operations, and low cost, SC circuits will be superior to the DSP circuits. The authors devised the SC circuit called parallel cyclic-type, which can further enhance the high-frequency and low power-consumption operation. The single-rate FIR and IIR filters have been proposed using the circuit. In this paper, the high frequency and low power-consumption FIR and IIR decimation filters using the SC parallel cyclic-type circuits are proposed. The effects of the finite gain bandwidth (GB product) of the operational amplifier and of the parasitic capacitance on the filter characteristics are analyzed. The proposed filters and the decimation filter by Franca et al. are constructed using discrete elements and the characteristics are examined. The characteristics are compared with the computer simulations. It is verified as a result that the proposed decimation filter has a much better performance than the filter by Franca et al. [ABSTRACT FROM AUTHOR]

This paper presents a design method of two-dimensional (2-D) perfect reconstruction filter banks for arbitrary sampling lattices. First, a design of 2-D N-th-band digital filters with arbitrary sampling lattices is shown. Next, the relation between the sampling matrix and the number of paths is presented and the band- limited region and the condition of delays are defined. From these conditions, the approximation problem is shown of the 2-D allpass filter whose 2-D N-th-band filter is composed and the characteristics of 2-D N-th-band filters are explained. Then 2-D analysis banks consist of 2-D discrete Fourier transform (DFT) and 2-D N-th-band filter which consists of some delays and 2-D interpolated allpass networks. To achieve the perfect reconstruction, by evaluating the aliasing component matrix, it is shown that the synthesis banks can also be constructed the same as the analysis bank. [ABSTRACT FROM AUTHOR]

This paper proposes an extension of the real-coefficient wave digital filter by Fettweis et al. (WDF) to the complex-coefficient WDF (CWDF) as well as a construction method to realize an arbitrary complex-coefficient transfer function. The first step of the proposed construction method is to synthesize the lossless reactance circuit containing the imaginary resistors (except for the input terminal) as an analog reference circuit by the continued-fraction expansion. In this study, the LC ladder network containing imaginary resistors is synthesized as the reference network, realizing the denominator polynomial of the transfer function. Then the state-variable representation is constructed and the numerator polynomial is realized by determining the tap coefficients to the external output, using the transform matrix. In this process, the reference network is transformed into WCDF, end the tap is formed considering the relation between incident/reflected waves and the terminal voltages. By this procedure, the required transfer function can be realized. Finally, the proposed method is compared to other construction methods and the low-sensitivity property of the proposed method is demonstrated. [ABSTRACT FROM AUTHOR]

A new design method for two-dimensional allpass filters to approximate the desired phase characteristic is proposed in this paper. Considering the denominator polynomial of the allpass transfer function, the design method via Hilbert transform is expanded to a two-dimensional ease with complex coefficients. When the Hilbert transform is used, a problem arises in that sometimes truncating coefficients cause the filter to be unstable. In this paper, in an unstable ease, the resultant frequency response is approximated as a low-order polynomial by using the Lagrange interpolation technique and the same procedures are repeated. Therefore, this proposed method ensures the stability of the designed filter because the coefficients of order higher than the desired order are small enough to be almost zero. [ABSTRACT FROM AUTHOR]

This paper presents the analysis of the roundoff error due to product quantization for the block state-space digital filter implemented with a digital signal processor (DSP) or a special-purpose LSI for filtering in one dimension (1-D) and two dimension (2-D). Here, it is assumed that a special-purpose LSI for filtering has two wordlengths, that is: 1) the external wordlength for the input signals, the output signals, the filter coefficients, and the state variables; and 2) the internal wordlength for the arithmetic logic unit (ALU) in that LSI. It is assumed also that the internal wordlength is longer than the external one. Two numerical examples are illustrated for a 2-D second-order filter and a 2-D (3, 3)-th-order filter. The results act as a guide to determine the internal wordlength and the external wordlength of a special-purpose LSI. Moreover, by setting the internal wordlength a few bits longer than the external wordlength, the roundoff error of block filtering can be reduced to from 20 through 60 percent compared with the nonblock filtering. [ABSTRACT FROM AUTHOR]

To extract a finite discrete signal from an infinite discrete signal, various window functions have been proposed in digital-signal processing. This paper proposes a method to design a window function by using the Remez method, which is a procedure to design a linear-phase FIR filter. A window function with an arbitrary sidelobe characteristic can easily be designed by setting a weighted function and using the same algorithm. Further, this paper describes an example of a procedure of designing a window function with a constant sidelobe amplitude decrease, and the procedure of designing a window function having the same sidelobe characteristic as sidelobe characteristics of convenient window function. The comparison of window functions designed by using the proposed method and conventional methods shows that the former is superior to the latter. [ABSTRACT FROM AUTHOR]

Control and protection equipment in power systems requires higher sensitivity and operational reliability to meet today's changing power system requirements. The voltage-measuring deviation requirement for advanced voltage and var control equipment is less than 0.1 percent under conditions of harmonic distortion in the voltage waveform and power-system frequency variation. Studies on digital signal processing suitable for electric power systems showed that these requirements are satisfied using fast sampling and very fast 32-bit floating point operations by a Digital Signal Process (DSP). This paper describes the design philosophy of a high-precision power system voltage-measuring method using fast sampled data. In addition, total voltage-measuring deviation characteristics under a combination of the techniques are described along with digital filter characteristics, frequency-measuring deviation characteristics, frequency variation versus gain-compensation characteristics of a digital filter, and peak value operating principles. [ABSTRACT FROM AUTHOR]

A new design method of an all-digital automatic gain control easy to implement is described and tested. The discretisation of the instantaneous gain provides a recursive form that merges the exponential function with the level detection. The first proposed circuit is well adapted for a software implementation. It comprises a simple control loop and two multipliers. It does neither contain digital filter nor divider and its setting only requires a loop gain parameter. Some tests were conducted on real digital audio signals with a dynamic range of 80 dB and they validate this approach. Under some conditions, the second circuit can even be simpler since it requires only one multiplier. It is well adapted to an field programmable gate array (FPGA) implementation for high speed signal processing. [ABSTRACT FROM AUTHOR]