Variable Finite Impulse Response Research Articles

Development of variable 2D FIR filter structures using farrow approximation and row-wise polyphase decomposition

This work proposes pre and post Farrow approximation of row-wise polyphase decomposed 2D finite impulse response (FIR) filters to achieve variability in 2D bandwidths with low implementation costs. The proposed method starts with realizing variable 2D filters using the 2D Farrow structure. The 2D Farrow filter structure is then row-wise polyphase decomposed and approximated in terms of fractional delay again to obtain the final set of coefficients. To illustrate the efficiency of the proposed methodology, design examples of variable circular and elliptical filters are provided in this paper. The simulation results show that the proposed methodology can result in variable 2D FIR filters with a considerable reduction in the number of multipliers w.r.t the existing approaches without much degradation in the performance parameters.

A Low Complexity and High Modularity Design for Continuously Variable Bandwidth Digital Filters

ABSTRACT Digital filters with variable bandwidth can be used for a variety of applications. Arbitrary change in the bandwidth of a digital Finite Impulse Response (FIR) filter can be acquired using sampling rate converters. In this paper, a sampling rate converter is proposed which is generated from Pascal structure, a fractional delay filter having low hardware complexity and high modularity. The proposed sampling rate converter requires lesser number of multipliers for implementation when compared with the sampling rate converters in the literature. A low pass filter having a single bandwidth sandwiched between two sampling rate converters can contribute multiple bandwidths in such a way that each bandwidth is an arbitrary variation of the original bandwidth. A two stage Frequency response masking approach (FRM) is used for the hardware efficient design of the original low pass filter. A low complexity and high modularity novel design for a continuously varying bandwidth of a digital FIR filter is proposed in this paper using the proposed sampling rate converter. The modularity of the Pascal structure can be used to control both pass band ripple as well as stop band attenuation of the continuously variable bandwidth FIR filter design. Different communication standards in a Software defined radio (SDR) channelizer is realized using the proposed design of continuously variable bandwidth filter.

Systolic architecture for adaptive block FIR filter for throughput using distributed arithmetic

In this paper, the design of distributed arithmetic (DA) finite impulse response (FIR) filter using block least mean square algorithm (BLMS) based on systolic array architecture with parallel data processing units is presented. A high level of parallelism is observed in the proposed work, improving the efficiency of variable coefficient FIR structure. The parallel look-up tables (LUT) in combination with the shift accumulator emulate multiply and accumulate operations. In order to reduce the number of clock cycles, B parallel LUTs are used, where B is the coefficient size. The block processing in BLMS Adaptive FIR Filter of block length L gives L times high throughput. This structure accepts block of input samples and generates block of output in each clock cycle. It requires less number of registers for computing filter output response and weight increment vector as memory reuse concept is used for implementing registers. This structure doesn’t require multiplexer. The designed DA based FIR filter is implemented on FPGA. The implementation results shows that the manuscript presents a high speed and low power architecture. The proposed structure provides 17.3 times less power and 9.5 times increase in throughput when compared to existing designs.

Design of narrow transition band variable bandwidth digital filter

This study presents a novel implementation technique for linear phase variable bandwidth finite impulse response (FIR) filters with a noticeable reduction in transition bandwidth as well as hardware complexity. In this proposition, concept of Farrow structure based design technique is effectively utilised; whereas the fixed sub-filters are constructed from a generalised interpolated bandpass method based low-pass FIR filter by means of different techniques such as interpolation, up-sampling and masking. Simulation results have shown the frequency response characteristics of several variable bandwidth FIR filters, designed with the help of the proposed architecture. Simulation results have shown a drastic reduction of transition bandwidth resulting from the proposed variable bandwidth FIR filters of up to ∼70–80%, when compared with other state-of-the-art filtering techniques, with a significant reduction in hardware complexity of up to ∼50%.

Closed-Form Design of Variable Fractional-Delay FIR Filters With Low or Middle Cutoff Frequencies

This paper aims to design variable fractional-delay (VFD) finite-impulse response (FIR) filters with controllable cutoff frequencies. Different with the existing designs, a particular ladder-shaped curve is selected as the desired transfer characteristic of the proposed design. Due to the fact that this particular transfer curve can be well approximated by the convolution windowed spectrum interpolation-based filter, the analytic formula of this filter can be further combined with the cubic spline interpolation and Taylor series expansion, thereby deriving a fast configuration procedure for all tap coefficients in the Farrow structure. Meanwhile, both the fractional delay and the cutoff frequency can be flexibly adjusted by this procedure. By means of theoretical analysis or numerical simulation, we proved that the proposed method is not only suitable to design those VFD FIR filters with low or middle cutoff frequencies, but also concurrently possesses high flexibility in performance adjustment and low complexity in coefficient configuration. Therefore, it is an appropriate supplement of the closed-form WLS design.

Design of efficient circularly symmetric two-dimensional variable digital FIR filters

Circularly symmetric two-dimensional (2D) finite impulse response (FIR) filters find extensive use in image and medical applications, especially for isotropic filtering. Moreover, the design and implementation of 2D digital filters with variable fractional delay and variable magnitude responses without redesigning the filter has become a crucial topic of interest due to its significance in low-cost applications. Recently the design using fixed word length coefficients has gained importance due to the replacement of multipliers by shifters and adders, which reduces the hardware complexity. Among the various approaches to 2D design, transforming a one-dimensional (1D) filter to 2D by transformation, is reported to be an efficient technique. In this paper, 1D variable digital filters (VDFs) with tunable cut-off frequencies are designed using Farrow structure based interpolation approach, and the sub-filter coefficients in the Farrow structure are made multiplier-less using canonic signed digit (CSD) representation. The resulting performance degradation in the filters is overcome by using artificial bee colony (ABC) optimization. Finally, the optimized 1D VDFs are mapped to 2D using generalized McClellan transformation resulting in low complexity, circularly symmetric 2D VDFs with real-time tunability.

繰り返し重み付き最小二乗法を用いた阻止域の複数要素が可変なFIRフィルタの準等リプル設計

Automatically dynamic measurement systems to measure object weights are used in logistics and food industry, etc. The systems are composed of belt conveyor and road cell, and is called checkweigher. Checkweighers have a problem that noises of error factor change according to speed of belt conveyor and installation surrounding. As a result, variable filters are better suited for checkweighers to reduce the noises after installation. In this paper, we propose a design method of quasi-equiripple variable linear-phase FIR (Finite Impulse Response) filters using iterative weighted least squares method in the frequency domain. The proposed variable filter has some piecewise high attenuations in the stopband, and can change multi-factor in the stopband characteristics and some notch frequencies using variable parameters. In the proposed variable filter, filter coefficients are approximated by polynomial using polynomial coefficients and variable parameters. The number of the polynomial coefficients increases when variable parameters are the plural number or polynomial orders are high. Therefore, we also propose a reduction method of the polynomial coefficients. The usefulness of the proposed design method is verified through the examples.

A Design Method for Variable Linear-Phase FIR Filters with Changing Multifactors for Checkweighers

Digital signal processing requires digital filters with variable frequency characteristics. A variable digital filter (VDF) is a filter whose frequency characteristics can be easily and instantaneously changed. In this paper, we present a design method for variable linear-phase finite impulse response (FIR) filters with multiple variable factors and a reduction method for the number of polynomial coefficients. The obtained filter has a high piecewise attenuation in the stopband. The stopband edge and the position and magnitude of the high piecewise stopband attenuation can be varied by changing some parameters. Variable parameters are normalized in this paper. An optimization methodology known as semidefinite programming (SDP) is used to design the filter. In addition, we present that the proposed VDF can be implemented using the Farrow structure, which suitable for real time signal processing. The usefulness of the proposed filter is demonstrated through examples.

Design of Variable Fractional-Delay FIR Differentiators

In this paper, the least-squares design of variable fractional-delay (VFD) finite impulse response (FIR) digital differentiators is proposed. The used transfer function is formulated so that Farrow structure can be applied to realize the designed system. Also, the symmetric characteristics of filter coefficients are derived, which leads to the complexity reduction by saving almost a half of the number of coefficients. Moreover, all the elements of related vectors or matrices for the optimal process can be represented in closed forms, which make the design easier. Design example is also presented to illustrate the effectiveness of the proposed method. Keywords—Differentiator, variable fractional-delay filter, FIR filter, least-squares method, Farrow structure.

Minimax Design of Variable Fractional-Delay FIR Digital Filters by Iterative Weighted Least-Squares Approach

In this letter, an iterative weighted least-squares (LS) approach is proposed for the design of variable fractional-delay (VFD) finite impulse response (FIR) digital filters in minimax sense. For deriving the elements of relevant matrices, there is no need for numerical integration or closed-form formulation and they obey given specifications. Comparing with the existing method, the proposed method does not lead to a misleading problem, and the performance of convergence is also better. Especially, it is found that the used LS weighting function is only dependent on the frequency, not on the tunable parameter, which makes it easier for the minimax design of VFD FIR digital filters.

Fast algorithms for designing variable FIR notch filters

AbstractThe paper presents fast algorithms for designing finite impulse response (FIR) notch filters. The aim is to design a digital FIR notch filter so that the magnitude of the filter has a deep notch at a specified frequency, and as the notch frequency changes, the filter coefficients should be able to track the notch fast in real time. The filter design problem is first converted into a convex optimization problem in the autocorrelation domain. The frequency response of the autocorrelation of the filter impulse response is compared with the desired filter response and the integral square error is minimized with respect to the unknown autocorrelation coefficients. Spectral factorization is used to calculate the coefficients of the filter. In the optimization process, the computational advantage is obtained by exploiting the structure of the Hessian matrix which consists of a Toeplitz plus a Hankel matrix. Two methods have been used for solving the Toeplitz‐plus‐Hankel system of equations. In the first method, the computational time is reduced by using Block–Levinson's recursion for solving the Toeplitz‐plus‐Hankel system of matrices. In the second method, the conjugate gradient method with different preconditioners is used to solve the system. Comparative studies demonstrate the computational advantages of the latter. Both these algorithms have been used to obtain the autocorrelation coefficients of notch filters with different orders. The original filter coefficients are found by spectral factorization and each of these filters have been tested for filtering synthetic as well as real‐life signals. Copyright © 2007 John Wiley & Sons, Ltd.

Design of variable and adaptive fractional order FIR differentiators

In this paper, the design problems of variable and adaptive fractional order finite impulse response (FIR) differentiators are investigated. First, the fractional differencing method and weighted least squares (WLS) approach are presented to design variable fractional order differentiators which can be implemented by the efficient Farrow structure. Next, an adaptive fractional order differentiator is developed and applied to estimate the parameters of 1/ f noise from the finite observation data set. The parameters are updated by using least mean squares (LMS) adaptive algorithm. Finally, the variable fractional order differentiator is used to reduce the error rate of handwritten signature verification system.

Closed-Form Design and Efficient Implementation of Variable Digital Filters with Simultaneously Tunable Magnitude and Fractional Delay

This paper proposes a closed-form solution for designing variable one-dimensional (1-D) finite-impulse-response (FIR) digital filters with simultaneously tunable magnitude and tunable fractional phase-delay responses. First, each coefficient of a variable FIR filter is expressed as a two-dimensional (2-D) polynomial of a pair of parameters called spectral parameters; one is for independently tuning the cutoff frequency of the magnitude response, and the other is for independently tuning fractional phase-delay. Then, the closed-form error function between the desired and actual variable frequency responses is derived without discretizing any design parameters such as the frequency and the two spectral parameters. Finally, the optimal solution for the 2-D polynomial coefficients can be easily determined through minimizing the closed-form error function. We also show that the resulting variable FIR filter can be efficiently implemented by generalizing Farrow structure to our two-parameter case. The generalized Farrow structure requires only a small number of multiplications and additions for obtaining any new frequency characteristic, which is particularly suitable for high-speed tuning.

Design and parallel implementation of FIR digital filters with simultaneously variable magnitude and non-integer phase-delay

Variable fractional-delay digital filters are useful in various signal processing applications. To perform both fractional-delay filtering and signal frequency selecting, variable fractional-delay filters must also have variable magnitude characteristics. This paper proposes a method for designing variable finite-impulse response (FIR) filters with both variable magnitude and variable noninteger phase-delay. First, the coefficients of a variable FIR filter are expressed as different 2-variable polynomials of a pair of spectral parameters; one is for varying magnitude response, and the other is for varying noninteger phase-delay. Then the optimal coefficients of the 2-variable polynomials are found by minimizing the total weighted squared error of the variable frequency response. Since the coefficients of the obtained variable FIR filter are the polynomials of the two spectral parameters, we can yield variable magnitude and variable noninteger phase-delay simultaneously or independently by substituting different spectral parameter values to the 2-variable polynomial coefficients. Finally, we show that the resulting variable FIR filter can be implemented in a parallel form, which is suitable for high-speed signal processing.

Weighted least-squares method for designing arbitrarily variable 1-D FIR digital filters

Variable digital filters with variable cutoff frequencies can be designed by frequency transformation methods. Such methods are simple, but they are not applicable to the design of variable filters with arbitrarily variable frequency responses. This paper proposes an efficient method for designing variable one-dimensional (1-D) finite-impulse-response (FIR) digital filters with arbitrarily variable magnitude characteristics and specified linear or nonlinear phase responses. First, each coefficient of the variable FIR filter is assumed to be a multi-dimensional (M-D) polynomial of spectral parameters that specify different variable magnitude characteristics. Then we present a pair of least-squares algorithms for finding the optimal polynomial coefficients by minimizing the weighted squared error between the desired variable frequency response and the actual frequency response. The first one is for designing 1-D FIR filters with variable magnitude response and linear-phase, and the second one is for designing variable 1-D FIR filters with variable magnitude response and nonlinear-phase. Although the first algorithm can be regarded as a special case of the second one, using the first one in the linear case can simplify the design significantly. The proposed methods are very straightforward and efficient for designing variable digital filters with arbitrarily variable magnitude responses and specified linear or nonlinear phases.