Design of FIR digital filters with prescribed flatness and peak error constraints using second-order cone programming

This paper studies the design of digital finite impulse response (FIR) filters with prescribed flatness and peak design error constraints using second-order cone programming (SOCP). SOCP is a powerful convex optimization method, where linear and convex quadratic inequality constraints can readily be incorporated. It is utilized in this study for the optimal minimax and least squares design of linear-phase and low-delay (LD) FIR filters with prescribed magnitude flatness and peak design error. The proposed approach offers more flexibility than traditional maximally-flat approach for the tradeoff between the approximation error and the degree of design freedom. Using these results, new LD specialized filters such as digital differentiators, Hilbert Transformers, Mth band filters and variable digital filters with prescribed magnitude flatness constraints can also be derived.     

A 3-D generalized direct PWM algorithm for multilevel converters

A three-dimensional (3-D) generalized direct pulse width modulation (PWM) algorithm is proposed for multilevel converters in a three-phase, four-wire system. It is proved to be equivalent to the newly proposed generalized 3-D space vector modulation (SVM). However, the direct PWM greatly simplifies the calculation process and is much easier to implement in digital controllers. The direct PWM can be used in all applications needing a 3-D control vector, such as active filters, uninterruptible power supplies, etc. Simulation and experimental results are given to show the validity of the proposed control strategy.     

任意型一维FIR数字滤波器设计新方法

本文介绍了一种设计任意型（宽带、窄带、低阶、高阶、低通、高通、带通、带阻）一维FIR数字滤波器新方法．给出设计不同类型滤波器的统一方法。各种类型滤波器脉冲响应的设计公式简单、计算方便。该方法消除了Gibbs现象．不仅克服了优化设计中收敛速度、设计精度及初值选取等问题，而且减少设计高阶滤波器的时间。最后，本文给出了各种类型滤波器设计的仿真结果。     

Image data compression using subband coding

A general reversive subband coding system with 2-D infinite impulse response filters is proposed. The system considered guarantees perfect image reconstruction (free of phase distortions). Application of wave digital filters is considered. A new technique of high-frequency source encoding is proposed. The experiments with real images prove high efficiency of the technique proposed.     

IIR数字滤波器仿真实现

数字滤波技术是数字信号处理的一个重要组成部分,滤波器的设计是信号处理的核心问题之一。本文分析了在MATLAB环境下无限脉冲响应（IIR）数字滤波器设计的设计方法及仿真实现。     

Design of High-Order Extrapolated Impulse Response FIR Filters with Signed Powers-of-Two Coefficients

Expensive multiplication operations can be replaced by simpler additions and hardwired shifters so as to reduce power consumption and area size, if the coefficients of a digital filter are signed power-of-two (SPT). As a consequence, FIR digital filters with SPT coefficients have been widely studied in the last three decades. However, most approaches for the design of FIR filters with SPT coefficients focus on filters with length less than 100. These approaches are not suitable for the design of high-order filters because they require excessive computation time. In this paper, an approach for the design of high-order filters with SPT coefficients is proposed. It is a two-step approach. Firstly, the design of an extrapolated impulse response (EIR) filter is formulated as a standard second-order cone programming (SOCP) problem with an additional coefficient sensitivity constraint for optimizing its finite word-length effect. Secondly, the obtained continuous coefficients are quantized into SPT coefficients by recasting the filter-design problem into a weighted least squares (WLS) sequential quadratic programming relaxation (SQPR) problem. To further reduce implementation complexity, a graph-based common subexpression elimination (CSE) algorithm is utilized to extract common subexpressions between SPT coefficients. Simulation results show that the proposed method can effectively and efficiently design high-order SPT filters, including Hilbert transformers and half-band filters with SPT coefficients. Experiment results indicate that 0.81N∼0.29N adders are required for 18-bit N-order FIR filters (N=335∼3261) to meet the given magnitude response specifications.     

Maxflat Fractional Delay IIR Filter Design

Fractional delay (FD) filters are an important class of digital filters and are useful in various signal processing applications. This paper discusses a design problem of FD infinite-impulse-response (IIR) filters with the maxflat frequency response in frequency domain. First, a flatness condition of FD filters at an arbitrarily specified frequency point is described, and then a system of linear equations is derived from the flatness condition. Therefore, a set of filter coefficients can be easily obtained by solving this system of linear equations. For a special case in which the frequency response is required to be maxflat at omega = 0 or pi , a closed-form expression for its filter coefficients is derived by solving a linear system of Vandermonde equations. It is also shown that the existing maxflat FD finite-impulse-response (FIR) and IIR filters are special cases of the FD IIR filters proposed in this paper. Finally, some examples are presented to demonstrate the effectiveness of the proposed filters.     

Low-power digital filtering using approximate processing

We present an algorithmic approach to the design of low-power frequency-selective digital filters based on the concepts of adaptive filtering and approximate processing. The proposed approach uses a feedback mechanism in conjunction with well-known implementation structures for finite impulse response (FIR) and infinite impulse response (IIR) digital filters. Our algorithm is designed to reduce the total switched capacitance by dynamically varying the filter order based on signal statistics. A factor of 10 reduction in power consumption over fixed-order filters is demonstrated for the filtering of speech signals     

基于广义Gabor变换的最优LOFDM系统的脉冲成形

LOFDM(Lattice Orthogonal Frequency Division Multiplexing )是时频弥散信道上的一种高速数据传输技术。但当LOFDM系统的脉冲成形滤波器不具有最优的时频局域化特性时,必将引入严重的ISI和/或ICI。因此脉冲成形滤波器的设计是最优LOFDM系统设计的重要组成部分。Strohmer和Beav(2001,2003)给出了一种LOFDM脉冲成形滤波器的设计方法,但是计算量较大。为此,该文提出了一种广义Gabor变换,通过构造广义紧致Gabor原子来完成最佳LOFDM脉冲成形滤波器的设计的数值实现。理论分析和仿真试验都证明该方法比Strohmer和Beaver给出的方法更简单有效。     

A simple and efficient design of variable fractional delay FIR filters

In this paper, a simple and efficient approach for designing one-dimensional variable fractional delay finite impulse response digital filters is proposed. Two matrix equations, based respectively on the weighted least-squares function of the optimum fixed fractional delay filter and the filter coefficient polynomial fitting, are formulated in tandem to form the design algorithm, which only has the computation complexity comparable with that of designing fixed finite impulse response digital filters. A design example is also given to justify the effectiveness and advantages of the proposed design method.     

Design of Two-Dimensional Pseudorotated Digital Filters Using Concept of Generalized Immittance Converter

A new realization procedure based on the concept of the generalized immittance converter (GIC) is proposed for two-dimensional (2D) pseudorotated digital filters that have circularly symmetric magnitude response characteristics. By applying a suitable transformation to a one-dimensional stable discrete transfer function, the 2D discrete transfer function of the corresponding pseudorotated filter is obtained. This transfer function is then realized by using a direct computer-based method. It is shown that four types of GIC pseudorotated filter structures can be obtained by interconnecting a few specific types of digital modules. The modularity and regularity nature of these filters make them attractive for very large-scale integration implementation.     

Digital compensation in IQ modulators using adaptive FIR filters

This paper discusses digital compensation for frequency-dependent transfer characteristics and implementation errors in digital PAM/continuous-phase frequency-shift keying (CPFSK) quadrature modulators. Recently, several methods have been proposed to digitally compensate for the shortcomings of the analog reconstruction filters in IQ modulators. While these methods have shown to be effective, they result in filters with long coefficients that are computationally demanding to implement on the DSP. Furthermore, the modulator needs to be taken offline while the precompensation filters are updated to reflect the changes in the I and Q channel characteristics. In this paper, a digital compensation method is proposed here using two adaptive finite-impulse response filters to compensate for the magnitude and phase characteristics of the analog reconstruction filters in the IQ modulator. The experimental results show that this technique is effective and lead to substantial improvement of the output envelope ripples.     

High-speed CMOS adder and multiplier modules for digital signalprocessing in a semicustom environment

For the realization of digital filters in a semicustom environment, high-performance adder and multiplier modules have been developed. These modules define the performance limits for digital finite impulse response (FIR) filters. The Gate Forest semicustom environment is a sea-of-gates-type transistor array. It supports the implementation of dynamic (domino) CMOS logic circuits. The circuit-design technique is applicable to compact high-speed designs. The realized dynamic adder architecture consists of a 2-b group adder and a Manchester carry chain (MCC). For an N-b addition this results in a N/2-b carry lookahead path. This dynamic adder scheme can be expanded into 4-b group adder modules. The multiplier module is a combination of a modified Booth-coded static adder array with a final dynamic MCC adder. The multiplier is clocked with a single (symmetric) clock signal. The clock signal is divided into a precharge pulse, in which the static part of the multiplier added array is evaluated, and an evaluation phase for the generation of the multiplication result (least significant bits). A 16-b×16-b multiplier based on this architecture runs with a 40-MHz system clock. The first chips have been processed in a 2-μm CMOS double-metal technology     

一种高性能内插滤波器的设计

在全数字接收机系统中,随着高阶调制解调技术的应用,传统内插滤波器的性能已不能满足要求。为此,通过研究一种多项式函数的频率响应,提出了一种高性能内插滤波器的设计方法。该方法在频域逼近的基础上,以线性加权的最小均方误差（MMSE）为优化准则,利用Matlab系统函数进行线性约束条件下的最优化迭代,设计非常灵活。仿真结果表明,该方法设计的内插滤波器性能明显优于常用的内插滤波器,尤其适合于高阶正交幅度调制（QAM）信号。     

The design and multiplier-less realization of software radio receivers with reduced system delay

This work studies the design and multiplier-less realization of a new software radio receiver (SRR) with reduced system delay. It employs low-delay finite-impulse response (FIR) and digital allpass filters to effectively reduce the system delay of the multistage decimators in SRRs. The optimal least-square and minimax designs of these low-delay FIR and allpass-based filters are formulated as a semi-definite programming (SDP) problem, which allows zero magnitude constraint at /spl omega/=/spl pi/ to be incorporated readily as additional linear matrix inequalities (LMIs). By implementing the sampling rate converter (SRC) using a variable digital filter (VDF) immediately after the integer decimators, the needs for an expensive programmable FIR filter in the traditional SRR is avoided. A new method for the optimal minimax design of this VDF-based SRC using SDP is also proposed and compared with traditional weight least squares method. Other implementation issues including the multiplier-less and digital signal processor (DSP) realizations of the SRR and the generation of the clock signal in the SRC are also studied. Design results show that the system delay and implementation complexities (especially in terms of high-speed variable multipliers) of the proposed architecture are considerably reduced as compared with conventional approaches.     

Realization of IIR LDM digital filters

A method is presented of realizing an infinite impulse response (IIR) digital filter (DF) using linear delta modulation (LDM) as a simple analog/digital (A/D) converter. This method makes the realization of IIR digital filters much simpler than that of conventional ones because it does not require hardware multipliers or a pulse code modulation (PCM) A/D converter. Compared to the finite impulse response (FIR) LDMDF, this IIR LDMDF requires significantly less computation time     

Design of stable IIR digital filter based on least P-power error criterion

In this paper, the least p-power error criterion is presented to design digital infinite impulse response (IIR) filters to have an arbitrarily prescribed frequency response. First, an iterative quadratic programming (QP) method is used to design a stable unconstrained one-dimensional IIR filter whose optimal filter coefficients are obtained by solving the QP problem in each iteration. Then, the proposed method is extended to design constrained IIR filters and two-dimensional IIR filters with a separable denominator polynomial. Finally, design examples of the low-pass filter are demonstrated to illustrate the effectiveness of the proposed iterative QP method.     

Realization of modular multidimensional complex digital filters using GIC concept

It is known that complex digital filters possess certain advantages over real digital filters in processing complex signals such as increased computational speed and efficiency. In this paper, a simple and systematic procedure which can be implemented through a computer program is presented for realizing a specific class of multidimensional (M-D) complex digital filters. The proposed filter structures are derived from analog reference configurations comprising generalized immittance converters and resistors by making use of wave concept. These filters possess many salient properties such as low noise, low sensitivity and capability of realizing multiple transfer functions simultaneously which are inherited from the reference analog filters they are derived from. These features make them attractive for very large-scale integrated (VLSI) implementation. It is shown that the proposed filter structures can be obtained directly from the specified M-D discrete transfer function without the need for realizing any analog reference configuration.     

Calculation of narrowband lowpass filters with finite impulse response

This study provides a review of digital filters known under the name “interpolated finite impulse response filters” (IFIR filters) that make it possible to create narrowband lowpass filters (LPF) with substantially reduced computational load and, consequently, a simpler design as compared with the conventional finite impulse response filters (FIR filters).     

Digital filters with implicit interpolated output

The composition of filtering and interpolation operators is applied to the design of digital filters that, optionally, may perform real-time incommensurate sampling rate conversion. This problem arises in applications where the interpolation times may not be known a priori and are calculated in real time. The proposed interpolating filter operators allow the designer to control the interpolation error through a trade-off between computing time and accuracy. The flexibility of the design is exemplified on a few digital communication applications: square root raised cosine filters for controlling the intersymbol interference through pulse shaping, a bandpass filter, and a differentiator