A simple odd-symmetric filter for digital broadcasting

A new odd-symmetric filter for ISI suppression and VSB transmission is proposed. The frequency response of the proposed filter is similar to that of an ideal raised-cosine filter, but in contrast to raised-cosine the new filter is realizable, e.g. using simple active filters. Simulation results show that concerning ISI suppression the new filter is significantly more efficient than the classical Butterworth or Chebyshev filters. The proposed filter can be also used as a VSB filter for TV modulators and demodulators.     

Generalized raised-cosine filters

Data transmission over bandlimited channels requires pulse shaping to eliminate or control intersymbol interference (ISI). Nyquist filters provide ISI-free transmission. Here we introduce a phase compensation technique to design Nyquist filters. Phase compensation can be applied to the square-root of any zero-phase bandlimited Nyquist filter with normalized excess bandwidth less than or equal to one. The resulting phase compensated square-root filter is also a Nyquist filter. In the case of a raised-cosine spectrum, the phase compensator has a simple piecewise-linear form. Such a technique is particularly useful to accommodate two different structures for the receiver, one with a filter matched to the transmitting filter and one without a matched filter. We also use the phase compensation technique to characterize a more general family of Nyquist filters which subsumes raised-cosine spectra. These generalized raised-cosine filters offer more flexibility in filter design. For instance, the rate of asymptotic decay of the filter impulse response may be increased, or the residual ISI, introduced by truncation of the impulse response, may be minimized. Design examples are provided to illustrate these choices     

Robust transceiver design for wideband MIMO radar utilizing a subarray antenna structure

In this paper, we investigate the possibility to suppress interference in wideband multiple-input multiple-output radar. The idea is to employ tunable filters at the transmitter and the receiver sides, and to derive filter coefficients that result in optimal transmitted signals from a system performance point of view, for a given radar scenario. The system performance is measured in signal-to-interference-and-noise ratio (SINR) at the receiver output, from which the filter properties are derived. The focus is to suppress active jamming interference, and especially deceptive jamming interference. We discuss two ways to derive the transmit and the receive filters. Each procedure utilizes two different power constraints related to the transmit filters. To incorporate imperfections in the given scenario, a robust extension to the design problem is proposed. Two different robust methods are evaluated: one that utilizes a Taylor series expansion of the SINR, and one that exploits a worst-case SINR maximization. Numerical validation illustrates the possibility to suppress interference without actually forming a spatial null in the direction towards interference, and the necessity to design transmit filters that are robust to uncertainties in the given scenario.     

On the use of interpolated second-order polynomials for efficientfilter design in programmable downconversion

Interpolated second-order polynomials (ISOPs) are proposed to design efficient cascaded integrator-comb (CIC)-based decimation filters for a programmable downconverter. It is shown that some simple ISOPs can effectively reduce the passband droop caused by CIC filtering with little degradation in aliasing attenuation. In addition, ISOPs are shown to be useful for simplifying halfband filters that usually follow CIC filtering. As a result, a modified halfband filter (MHBF) is introduced which is simpler than conventional halfband filters. The proposed decimation filter for programmable downconverter is a cascade of a CIC filter, an ISOP, MHBFs, and a programmable finite impulse response filter. A procedure for designing the decimation filter is developed. In particular, an optimization technique that simultaneously designs the ISOP and programmable FIR filters is presented. Design examples demonstrate that the proposed method leads to more efficient programmable downconverters than existing ones     

A design method of multidimensional linear-phase paraunitary filterbanks with a lattice structure

A lattice structure of multidimensional (MD) linear-phase paraunitary filter banks (LPPUFBs) is proposed, which makes it possible to design such systems in a systematic manner. Our proposed structure can produce MD-LPPUFBs whose filters all have the region of support 𝒩(MΞ), where M and Ξ are the decimation and positive integer diagonal matrices, respectively, and 𝒩(N) denotes the set of integer vectors in the fundamental parallelepiped of a matrix N. It is shown that if 𝒩(M) is reflection invariant with respect to some center, then the reflection invariance of 𝒩(MΞ) is guaranteed. This fact is important in constructing MD linear-phase filter banks because the reflection invariance is necessary for any linear-phase filter. Since our proposed system structurally restricts both the paraunitary and linear-phase properties, an unconstrained optimization process can be used to design MD-LPPUFBs. Our proposed structure is developed for both an even and an odd number of channels and includes the conventional 1-D system as a special case. It is also shown to be minimal, and the no-DC-leakage condition is presented. Some design examples show the significance of our proposed structure for both the rectangular and nonrectangular decimation cases     

MIMO CDMA antenna system for SINR enhancement

We present a system to enhance signal-to-interference plus noise ratio (SINR) for multiple-input-multiple-output (MIMO) direct-sequence code-division multiple-access (DS/CDMA) communications in the downlink for frequency-selective fading environments. The proposed system utilizes a transmit antenna array at the base station and a receive antenna array at the mobile station with finite-impulse response filters at both the transmitter and receiver. We arrive at our system by attempting to find the optimal solution to a general MIMO antenna system. A single user joint optimum scenario and a multiuser SINR enhancement scenario are derived. In addition, a simplified one-finger receiver structure is introduced. Numerical results reveal that significant system performance and capacity improvement over conventional approaches are possible. We also investigate the sensitivity of the proposed system to channel estimation errors.     

A family of pulse-shaping filters with ISI-free matched andunmatched filter properties

The raised-cosine pulse-shaping filter plays an important role in digital communications due to its intersymbol interference (ISI)-free property. The ISI-free property holds after matched filtering is performed. In this letter, we propose a new family of pulse-shaping filters. These filters are ISI free with or without matched filtering. Using these new pulse-shaping filters, the computational load, and therefore the hardware cost in demodulation for modem design, might be reduced in some applications     

L(p) norm design of stack filters.

Addresses the problem of designing optimal stack filters by employing an L(p) norm of the error between the desired signal and the estimated one. It is shown that the L(p) norm can be expressed as a linear function of the decision errors at the binary levels of the filter. Thus, an L(p)-optimal stack filter can be determined as the solution of a linear program. The conventional design of using the mean absolute error (MAE), therefore, becomes a special ease of the general L(p) norm-based design developed here. Other special cases of the proposed approach, of particular interest in signal processing, are the problems of optimal mean square error (p=2) and minimax (p-->infinity) stack filtering. Since an Linfinity optimization is a combinatorial problem, with its complexity increasing faster than exponentially with the filter size, the proposed L(p ) norm approach to stack filter design offers an additional benefit of a sound mathematical framework to obtain a practical engineering approximation to the solution of the minimax optimization problem. The conventional MAE design of an important subclass of stack filters, the weighted order statistic filters, is also extended to the L(p) norm-based design. By considering a typical application of restoring images corrupted with impulsive noise, several design examples are presented, to illustrate the performance of the L(p)-optimal stack filters with different values of p. Simulation results show that the L(p)-optimal stack filters with p=/>2 provide a better performance in terms of their capability in removing impulsive noise, compared to that achieved by using the conventional minimum MAE stack filters.     

卫星导航接收机时域窄带干扰抑制滤波器设计与性能分析

针对卫星导航接收机时域窄带干扰的有效抑制问题,本文首先给出二阶格型IIR陷波器参数设计方法,通过陷波带宽的定量调整,既可以有效抑制窄带干扰,又可以降低卫星信号的失真;其次推导了二阶IIR格型陷波器相关输出信干噪比改善因子的闭合表达式,该表达式相比干扰抑制后信干噪比的改善,更为直观地反映了陷波器对卫星导航信号的影响。理论分析和仿真实验,二阶格型IIR陷波器相关输出信干噪比改善因子与陷波器的带宽参数有关,而与陷波频率无关,且二阶格型IIR陷波器的性能优于最优线性预测Wiener滤波器、最优线性插值Wiener滤波器、五系数FIR滤波器以及二阶直接型IIR陷波器。      

Two-dimensional FlR filter design using matrix dilation approach

This paper develops an approach for the optimal design of two-dimensional (2-D) finite impulse response (FIR) filters based on the minimization of a new performance index. The approach gives analytical expressions for the optimal solution and offers a two-parameter family of suboptimal filters. It is shown that the conventional least square solutions is a member of this family. The approach is based on a result in linear algebra, and used in robust control theory, known as the dilation equation. An efficient numerical algorithm for solving the filter design problem using the dilation equation is proposed, and some techniques for choosing the design parameters are discussed. Finally, some examples are shown illustrating the flexibility of the design using the new approach     

Design of FIR filters with reduced computations

The performance of a symmetric nonrecursive filter can be improved by multiple use of the same filter. The method is based on an Amplitude Change Function (ACF). An approach to the design of nonrecursive filters using an ACF is discussed in this paper. The prototype filter chosen is a Recursive Running Sum (RRS) filter which does not require any multipliers for its implementation. The required filter specifications are met by multiple use of the RRS filters. The overall filter requires a much smaller number of multiplications and adders than the one designed using the conventional method. It is shown that this method provides reduced noise due to coefficient quantization and product quantization compared with the conventional design technique.     

Design of IIR orthogonal wavelet filter banks using lifting scheme

The lifting scheme is well known to be an efficient tool for constructing second generation wavelets and is often used to design a class of biorthogonal wavelet filter banks. For its efficiency, the lifting implementation has been adopted in the international standard JPEG2000. It is known that the orthogonality of wavelets is an important property for many applications. This paper presents how to implement a class of infinite-impulse-response (IIR) orthogonal wavelet filter banks by using the lifting scheme with two lifting steps. It is shown that a class of IIR orthogonal wavelet filter banks can be realized by using allpass filters in the lifting steps. Then, the design of the proposed IIR orthogonal wavelet filter banks is discussed. The designed IIR orthogonal wavelet filter banks have approximately linear phase responses. Finally, the proposed IIR orthogonal wavelet filter banks are applied to the image compression, and then the coding performance of the proposed IIR filter banks is evaluated and compared with the conventional wavelet transforms.     

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.     

Closed-Form Design of Half-Sample Delay IIR Filter Using Continued Fraction Expansion

In this paper, the closed-form design of half-sample delay infinite-impulse response (IIR) filter is presented. First, the continued fraction expansion (CFE) and its recursive computation are reviewed briefly. Then, the CFE of square root function is applied to design half-sample delay IIR filters with various orders. The comparisons with conventional maximally flat half-sample delay all-pass and Lagrange filters are made and implementation issue is also addressed. Next, the designed half-sample delay filter is used to reduce the approximation error of the conventional IIR Simpson integrator, to design half-band and diamond shaped filters, and to magnify the digital image. Finally, several numerical examples are illustrated to demonstrate the effectiveness of the proposed design method     

The classification and associative memory capability of stackfilters

The notion of the on-set of a positive Boolean function is used to classify stack filters into three different types, called decreasing, increasing, and mixed. The associative memory capability of each of these three types of stack filters is then investigated. The associative memory of a stack filter is defined to be the set of root signals of that filter. In a class of stack filters in which each filter's root set contains a desired set of patterns, those filters whose root sets have the smallest cardinality are said to be minimal among all filters in that class for that set of patterns. Some learning schemes are proposed to find minimal decreasing and increasing stack filters. It is also shown that, for any specified set of patterns, there is always a mixed stack filter which is minimal when one considers all stack filters which preserve those patterns. In this sense, mixed stack filters are always at least as good as decreasing or increasing stack filters     

Time-domain modified DFT modulated filter banks for multi-carrier transceiver systems

A time domain designing method is proposed for discrete Fourier transform （DFT） modulated filter banks （DFT-FBs） for application in multi-carrier transceiver systems. Instead of using the time-reversed pair limitation between the transmitting /receiving filter pair, the receiving filters in the proposed filter banks are derived from transmitting filters in accordance with the Moore-Penrose generalized inverse matrix. It can be freely obtained to design the transmitting prototype filter, which mainly affects the level of spectral containment. Furthermore, the symbol error rate （SER） performance of the proposed filter bank based trans-multiplexer with one tap equalizer is investigated in ideal channel and multi-path channel environments respectively. Simulation shows that the proposed approach can achieve significant SER reductions when square root raised cosine （RRC） prototype filter is used for comparing with the orthogonal frequency division multiplexing （OFDM） and the general DFT-FBs based applications.     

MIMO Radar Waveform Optimization With Prior Information of the Extended Target and Clutter

The concept of multiple-input multiple-output (MIMO) radar allows each transmitting antenna element to transmit an arbitrary waveform. This provides extra degrees of freedom compared to the traditional transmit beamforming approach. It has been shown in the recent literature that MIMO radar systems have many advantages. In this paper, we consider the joint optimization of waveforms and receiving filters in the MIMO radar for the case of extended target in clutter. A novel iterative algorithm is proposed to optimize the waveforms and receiving filters such that the detection performance can be maximized. The corresponding iterative algorithms are also developed for the case where only the statistics or the uncertainty set of the target impulse response is available. These algorithms guarantee that the SINR performance improves in each iteration step. Numerical results show that the proposed methods have better SINR performance than existing design methods.      

Optimal design of two-channel nonuniform-division FIR filter bankswith -1, 0, and +1 coefficients

This paper deals with the optimal design of two-channel nonuniform-division filter (NDF) banks whose linear-phase FIR analysis and synthesis filters have coefficients constrained to -1, 0, and +1 only. Utilizing an approximation scheme and a weighted least squares algorithm, we present a method to design a two-channel NDF bank with continuous coefficients under each of two design criteria, namely, least-squares reconstruction error and stopband response for analysis filters and equiripple reconstruction error and least-squares stopband response for analysis filters. It is shown that the optimal filter coefficients can be obtained by solving only linear equations. In conjunction with the proposed filter structure, a method is then presented to obtain the desired design result with filter coefficients constrained to -1, 0, and +1 only. The effectiveness of the proposed design technique is demonstrated by several simulation examples     

Broadband Beamforming Using TDL-Form IIR Filters

Conventional broadband beamforming structures make use of finite-impulse-response (FIR) filters in each channel. Large numbers of coefficients are required to retain the desired signal-to-interference-plus-noise-ratio (SINR) performance as the operating bandwidth increases. It has been proven that the optimal frequency-dependent array weighting of broadband beamformers could be better approximated by infinite-impulse-response (IIR) filters. However, some potential problems, such as stability monitoring and sensitivity to quantization errors, of the IIR filters make the implementation of the IIR beamformers difficult. In this paper, new broadband IIR beamformers are proposed to solve these problems. The main contributions of this paper include 1) the Frost-based and generalized sidelobe canceller (GSC)-based broadband beamformers utilizing a kind of tapped-delay-line-form (TDL-form) IIR filters are proposed; 2) the combined recursive Gauss-Newton (RGN) algorithm is designed to compute the feedforward and feedback weights in the Frost-based implementation; and 3) in the GSC-based structure, the unconstrained RGN algorithm is customized for the TDL-form IIR filters in the adaptive beamforming part. Compared with the beamformer using direct-form IIR filters, the new IIR beamformers offer much easier stability monitoring and less sensitivity to the coefficient quantization, while comparable SINR improvement over the conventional FIR beamformer is achieved     

Closed-Form Design of Generalized Maxflat$R$-Regular FIR$M$th-Band Filters Using Waveform Moments

$M$th-band filters have found numerous applications in multirate signal processing systems, filter banks, and wavelets. In this paper, the design problem of generalized maxflat$R$-regular finite impulse response (FIR)$M$th-band filters with a specified integer group delay at$ omega =0 $is considered, and the closed-form expression for its impulse response is presented. The filter coefficients are directly derived by solving a linear system of Vandermonde equations that are obtained from the regularity condition of the maxflat$R$-regular FIR$M$th-band filters via the blockwise waveform moments. Differing from the conventional FIR$M$th-band filters with exactly linear phase responses, the generalized FIR$M$th-band filters proposed in this paper have an arbitrarily specified integer group delay at$ omega =0 $. Moreover, a new efficient implementation of the generalized maxflat$R$-regular FIR$M$th-band filters is proposed by making use of the relationship between the filter coefficients in the closed-form solution. Finally, several design examples are presented to demonstrate the effectiveness of the proposed FIR$M$th-band filters.