Fast practical design of 2-D digital filters

This paper discusses a simple method for designing 2-D digital filters. The method can give linear phase 2-D filters with rather low computation cost, and can be generalized to multi-dimensional filtering applications. Examples are given to show its practicability. Northwest Telecommunication Engineering Institute     

Fast Parallel Approach for 2-D DHT-Based Real-Valued Discrete Gabor Transform

Two-dimensional fast Gabor transform algorithms are useful for real-time applications due to the high computational complexity of the traditional 2-D complex-valued discrete Gabor transform (CDGT). This paper presents two block time-recursive algorithms for 2-D DHT-based real-valued discrete Gabor transform (RDGT) and its inverse transform and develops a fast parallel approach for the implementation of the two algorithms. The computational complexity of the proposed parallel approach is analyzed and compared with that of the existing 2-D CDGT algorithms. The results indicate that the proposed parallel approach is attractive for real time image processing.      

基于2-DGabor滤波器的光学定穴体表特征提取方法

取穴准确性是决定针灸效果的最基本要求,这就需要对取穴体表特征进行精确地定位。文中提出一种新的人体体表特征定位的光学方法,在光学检测平台上通过相机采集不同方向的图像,选取合适的Gabor 滤波器参数,得到图像的强度响应并提取局部极大值,从而获得定穴体表轮廓特征。为验证该方法的有效性和精度,采用Sobel 算子、Canny 算子、LoG 算子以及Gabor 滤波器分别对灰度图像和二值图像进行特征提取。通过对比和分析,发现经过Gabor 函数滤波后得到的图像轮廓是连续且最清晰的;Gabor 函数对二值图像的滤波效果优于对灰度图像。实验结果表明,所提出的方法能精确快速地定位体表轮廓特征,为进一步利用轮廓特征提取定穴体表特征点以及研究穴位光学定位方法奠定基础。     

A weighted least-squares method for the design of stable 1-D and2-D IIR digital filters

We present a new approach to the least-squares design of stable infinite impulse response (IIR) digital filters. The design is accomplished by using an iterative scheme in which the denominator polynomial obtained from the preceding iteration is treated as a part of the weighting function, and each iteration is carried out by solving a standard quadratic programming problem that yields a stable rational function. When the iteration converges, a stable and truly least-squares solution is obtained. The method is then extended to address the least-squares design of stable IIR two-dimensional (2-D) filters. Examples are included to illustrate the proposed design techniques     

Electronically scanned RF-to-bits beam aperture arrays using 2-D IIR spatially bandpass digital filters

A beamforming system based on two-dimensional (2-D) spatially bandpass infinite impulse response (IIR) plane wave filtering is presented in a multi-dimensional signal processing perspective and the implementation details are discussed. Real-time implementation of such beamforming systems requires modeling of computational electromagnetics for the antennas, radio frequency (RF) analog design aspects for low-noise amplifiers (LNAs), mixed-signal aspects for signal quantization and sampling and finally, digital architectures for the spatially bandpass plane wave filters proposed in Joshi et al. (IEEE Trans Very Large Scale Integr Syst 20(12):2241–2254, 2012). Multi-dimensional spatio-temporal spectral properties of down-converted RF plane wave signals are reviewed and derivation of the spatially bandpass filter transfer function is presented. An example of a wideband antipodal Vivaldi antenna is simulated at 1 GHz. Potential RF receiver chains are identified including a design of a tunable combline microstrip bandpass filter with tuning range 0.8–1.1 GHz. The 1st-order sensitivity analysis of the beam filter 2-D $\mathbf z $ -domain transfer function shows that for a 12-bits of fixed-point precision, the maximum percentage error in the 2-D magnitude frequency response due to quantization is as low as $0.3\,\%$ . Monte-Carlo simulations are used to study the effect of quantization on the bit error rate (BER) performance of the beamforming system. 5-bit analog to digital converter (ADC) precision with 8-bit internal arithmetic precision provides a gain of approximately 16 dB for a BER of $10^{-3}$ with respect to the no beamforming case. ASIC Synthesis results of the beam filter in 45 nm CMOS verifies a real time operating frequency of 429 MHz.     

Approximation of complex IIR bandpass filters without arithmetic symmetry

Complex transfer functions are not restricted to having complex-conjugate symmetry in the frequency-domain, as is the case for real filters. This gives them more flexibility when they are used in communication systems with complex signals, such as intermediate frequency signals of wireless communication systems. This paper describes a set of algorithms and procedures that can be used in solving the approximation problem involved in deriving complex infinite-impulse-response bandpass transfer functions directly, without the requirement of first designing a real-transfer-function prototype filter, which is then frequency translated. Because the requirement for a real prototype filter is eliminated, the filters need not have arithmetic symmetry; this results in superior stopbands with smaller filter orders. The procedures can be used for both continuous and discrete-time filters, can allow for arbitrary stopband specifications, and can be used for either equi-ripple or monotonic passbands.     

Fast realisation of 2-D digital filters using logarithmic number systems

Previous papers of mine have discussed the approximation of 2-D digital filter coefficients with algebraic sums of integer powers of the base in a logarithmic number system. The results already obtained suggest a sequential memory-oriented realisation which is faster than the standard implementation.     

Design of 1-D and 2-D IIR eigenfilters

An effective method is proposed for the design of recursive digital filters in the time/spatial domain. The method is based on the computation of an eigenvalue and its corresponding eigenvector of an appropriate real symmetric and positive-definite matrix derived from the objective error function of the impulse response in the least-squares sense. The method can be used to design 1D IIR digital filters as well as 2D IIR digital filters. The method is easy and the performance is comparable to those of the existing methods. One of the main advantages of the proposed method is that the solution is obtained directly without the need for iteration     

New adaptive complex IIR filters and their application in OFDM systems

In this article, very low sensitivity variable complex filter (VCF) sections are developed. They have two important advantages: extremely low passband sensitivity and independent tuning of the bandwidth and the central frequency over a wide frequency range. The first advantage provides resistance to quantization effects, while the second one gives a better digital signal processing quality and extends the area of possible applications of the developed filters. Based on the proposed VCF sections an adaptive complex system is designed which demonstrates very fast convergence and low computational complexity. This system is applied for narrowband interference cancellation in multiband orthogonal frequency division multiplexing receivers and wideband noise cancellation in OFDM receivers. It is experimentally verified that a better signal-to-noise ratio and signal-to-interference ratio can be achieved using the proposed adaptive complex filtering scheme.     

Foreground text segmentation in complex color document images using Gabor filters

Extraction of foreground contents in complex background document images is very difficult as background texture, color and foreground font, size, color, tilt are not known in advance. In this work, we propose a RGB color model for the input of complex color document images. An algorithm to detect the text regions using Gabor filters followed by extraction of text using color feature luminance is developed too. The proposed approach consists of three stages. Based on the Gabor features, the candidate image segments containing text are detected in stage-1. Because of complex background, certain amount of high frequency non-text objects in the background are also detected as text objects in stage-1. In stage-2, certain amount of false text objects is dropped by performing the connected component analysis. In stage-3, the image segments containing textual information, which are obtained from the previous stage are binarized to extract the foreground text. The color feature luminance is extracted from the input color document image. The threshold value is derived automatically using this color feature. The proposed approach handles both printed and handwritten color document images with foreground text in any color, font, size and orientation. For experimental evaluations, we have considered a variety of document images having non-uniform/uniform textured and multicolored background. Performance of segmentation of foreground text is evaluated on a commercially available OCR. Evaluation results show better recognition accuracy of foreground characters in the processed document images against unprocessed document images.     

Design of stable IIR filters in the complex domain by automaticdelay selection

A major problem encountered when designing infinite impulse response (IIR) filters in the complex domain is to ensure that the filter is stable. Instability occurs frequently when the IIR filter approximates the inverse of a nonminimum phase system. This is often the case for equalization filters. Addition of delay to the target frequency response can result in a stable filter. However, to date, delay selection has been a matter of trial and error. The article presents an automated method for finding the delay     

A new approach to the design of complex all-pass IIR digital filters

A new method is proposed for designing complex all-pass IIR filters, the all-pass IIR filters with complex coefficients, in this paper. By minimizing the integration of certain square phase error over interested frequencies, an eigenvector of an appropriate real, symmetric and positive-definite matrix is computed to get the filter coefficients. The stability is achieved by specifying properly the desired phase specifications. If an appropriate iterative process is used, equiripple complex all-pass filter design can be obtained. The method is simple and the performance is comparable to the existing methods. Several examples are presented to demonstrate the effectiveness of the approach.     

Design of IIR digital filters using complex allpass network based on eigenvalue problem

A new design method is presented for complementary IIR digital filters with given magnitude specifications based on the eigenvalue problem, which are composed of a single complex allpass section.<>     

A Systolic Array 2-D IIR Broadband RF Beamformer

A systolic architecture is proposed for the real-time implementation of broadband 2-D IIR beam filters having applications in ultra-wideband (UWB) radio frequency (RF) antenna arrays. Real-time throughputs of one-frame-per-clock-cycle are achieved. A finite-difference time-domain computational electromagnetic model of a typical indoor propagation environment is used to illustrate that the method significantly reduces the bit error rate of the simulated communication system in the presence of multi-user interference, thereby demonstrating the potential application of the architecture in RF communications.      

Stable quarter-plane 2-D lattice filters

The stability of the two-dimensional quarter-plane lattice filter developed by Parker and Kayran (1984) is not guaranteed. Their lattice filter is potentially unstable unless a number of conditions are satisfied. The validity of these conditions are difficult to test. Three different lattice filter structures which are structurally stable for all parameters are presented.<>     

Realization of 2-D analogue filters

In this note a two-dimensional (2-D) analogue filter realization is presented. The structure requires only analogue devices and line delays. It can be utilized to realize any order filter, however, to demonstrate the approach a 2 × 2 filter structure is presented.     

Design of IIR notch filters with different passband gains

A method is proposed for the design of infinite-duration impulse response (IIR) notch filters with different passband gains using the standard lowpass IIR digital-filter design methods. This method satisfies the notch-frequency specification exactly and realises a rejection bandwidth, defined by the frequencies at which the gain is 3 dB below the lower of the two passband gains, which is smaller than that specified. Illustrative examples are given     

Designing IIR filters with a given 3-dB point

Often in infinite impulse response (IIR) filter design, our critical design parameter is the cutoff frequency at which the filter's power decays to half (-3 dB) the nominal passband value. This article presents techniques that aid in the design of discrete-time Chebyshev and elliptic filters given a 3-dB attenuation frequency point. These techniques place Chebyshev and elliptic filters on the same footing as Butterworth filters, which traditionally have been designed for a given 3-dB point. The result is that it is easy to replace a Butterworth design with either a Chebyshev or an elliptic filter of the same order and obtain a steeper rolloff at the expense of some ripple in the passband and/or stopband of the filter.     

Mixed microwave-digital and multi-rate approach for wideband beamforming applications using 2-D IIR beam filters and nested uniform linear arrays

The presented work explores novel methods for synthesizing approximately frequency independent array factors at lower hardware complexity for wideband beamforming applications. The proposed approach employs 2-D infinite impulse response (IIR) digital beam filters together with nested uniform linear arrays (ULAs). The array is designed to have multiple levels of nesting. Each level of nesting consists of a ULA covering a temporal subband of the incident wideband signal. The use of nested arrays provides the required aperture size using a smaller number of elements compared to using a single ULA to capture the entire wideband signal. The use of different levels of nesting allows the operation of the digital processor for each sub-band at different clock rates. This is a hierarchical approach that saves both digital VLSI hardware and power consumption. The 2-D IIR digital beam filters that process each subband signal from each of the nested subarray achieves wideband beamforming. Simulations illustrate approximately frequency independent passbands as required in wideband beamforming.     

Design of IIR digital filters in the complex domain by transforming the desired response

In this paper, we present a new design method of infinite impulse response (IIR) digital filters with quasi-equiripple absolute error in the complex domain. This method is based on solving a least squares solution iteratively. At each iteration, the desired response for the least squares approximation is transformed to have equiripple error. This algorithm is efficient because there is no need for any initial value or complex optimization algorithm. By this method, a quasi-equiripple solution is obtained very quickly with less computational complexity. Moreover, by multiplying an arbitrary weighting function on the desired responses of passband and stopband, respectively, the error at the passband and stopband can be controlled. Finally, we show some examples to validate the proposed method.