A low-pass notch filter for bioelectric signals

Many bioelectric signals have relatively low-frequency content, but measurement devices are susceptible to power-line interference. The Type II Chebyshev low-pass filter can simultaneously perform the required low-pass filtering and removal of the narrowband interference. This filter has transfer-function zeros which result in zero gain (- infinity dB) at specific 'null' frequencies. A procedure for the low-pass filter design makes the first null frequency a design parameter so that the notch can occur at the interference frequency.<>     

Eigenfilter Approach to the Design of One-Dimensional and Multidimensional Two-Channel Linear-Phase FIR Perfect Reconstruction Filter Banks

We present an eigenfilter-based approach for the design of two-channel linear-phase FIR perfect-reconstruction (PR) filter banks. This approach can be used to design 1-D two-channel filter banks, as well as multidimensional nonseparable two-channel filter banks. Our method consists of first designing the low-pass analysis filter. Given the low-pass analysis filter, the PR conditions can be expressed as a set of linear constraints on the complementary-synthesis low-pass filter. We design the complementary-synthesis filter by using the eigenfilter design method with linear constraints. We show that, by an appropriate choice of the length of the filters, we can ensure the existence of a solution to the constrained eigenfilter design problem for the complementary-synthesis filter. Thus, our approach gives an eigenfilter-based method of designing the complementary filter, given a “predesigned” analysis filter, with the filter lengths satisfying certain conditions. We present several design examples to demonstrate the effectiveness of the method.      

Minimum-phase CCD transversal filters

The calculated and measured response of a minimum-phase CCD low-pass transversal filter is compared to a linear-phase design with the same magnitude characteristics. It is shown that the minimum-phase design can offer up to an order of magnitude improvement in group delay, and is also less sensitive to transfer inefficiency and tap-weight error than the linear-phase design.     

巴特沃斯数字陷波滤波器的设计

随着数字技术的发展,数字滤波器在许多领域得到广泛的应用。研究一种在Matlab语言环境下设计IIR数字陷波滤波器的方法,在数字陷波滤波器设计过程中,先进行模拟低通滤波器的设计,然后进行模拟低通/模拟带阻滤波器转换,最后采用双线性变化法将模拟陷波滤波器转化成数字陷波滤波器。提出一种用所有零点和极点来表达数字陷波器传递函数的方法,同时给出以巴特沃斯模拟低通为原型设计数字陷波滤波器的程序。     

Tunable/adaptive second-order IIR notch filter

A modified second-order infinite impulse response (IIR) notch filter with constrained poles and zeros is presented to eliminate or retrieve sinusoids embedded in a broadband signal. Such a filter is ideally suited to either parallel or cascaded implementation. Two classes of problems are considered. The first is where the sinusoidal frequencies are known a priori. For this case a straightforward design procedure based on a set of design characteristic graphs is used to select tunable notch filter parameters. An interesting property of the notch filter model is that it can be converted to a line enhancer by interchanging the position of the poles and zeros. The second type of problem arises when the sinusoidal frequencies are unknown and possibly varying with time. This means that an adaptive solution is required and an important consideration is the parameter estimation accuracy. For this purpose, the paper derives the Cramer–Rao lower bound for the adaptive cascaded notch filter using a frequency-domain approach. Some simulation results are included to demonstrate the effectiveness of the proposed adaptive notch filter.     

自跟踪陷波器

本文提出一种自动调谐陷波器,其陷波中心频率自动跟踪市电频率或某一外加干扰频率,以抑制其干扰.陷波器的谐振电路由LC组成,而电感L是用普遍阻抗转换器(GIC)来实现,GIC的端接电阻为压控MOS管电阻,因此可以用一电压控制此电阻以改变电感值,进而控制陷波频率.这种陷波电路可用于抑制市电频率的干扰噪声并防止测量或数据采集系统中前置放大器的饱和.实验结果表明在频率从4555Hz,其陷波频率跟踪精度优于0.5Hz,而陷波深度(串模抑制比)为3040dB.     

Minimax design of adjustable-bandwidth linear-phase FIR filters

This paper considers the design of digital linear-phase finite-length impulse response (FIR) filters that have adjustable bandwidth(s) whereas the phase response is fixed. For this purpose, a structure is employed in which the overall transfer function is a weighted linear combination of fixed subfilters and where the weights are directly determined by the bandwidth(s). Minimax design techniques are introduced which generate globally optimal overall filters in the minimax (Chebyshev) sense over a whole set of filter specifications. The paper also introduces a new structure for bandstop and bandpass filters with individually adjustable upper and lower band edges, and with a substantially lower arithmetic complexity compared to structures that make use of two separate adjustable-bandwidth low-pass and high-pass filters in cascade or in parallel. Design examples are included in the paper.     

An analytical procedure for critical frequency tuning of FIR filters

A novel analytical procedure for the tuning of finite-impulse response (FIR) filters is introduced. The tuning procedure adjusts a single frequency of the frequency response to the desired value while preserving the nature of the filter. The impulse responses of the original and of the final filter are related by the transformation matrix. Two examples in the analytical design of notch FIR filters demonstrate the usefulness of the proposed tuning procedure.     

Design of doubly complementary filters with approximate linearphase

A new procedure for the design of a real doubly complementary (DC) pair of digital filters obtained from an all-pass structure is presented. The filter design is based on a zero-phase FIR filter design with multi-band frequency specifications and approximate linear-phase characteristic. The resulting complex or real all-pass filter structure is guaranteed to be stable. Some examples illustrating the design method including comparisons with conventional approximately linear phase IIR filters are also shown     

一种满足精确重建条件的多采样率滤波器组的实现方法

多采样率滤波器组可以通过对线性相位低通原型滤波器进行余弦调制来实现，本文给出了一咱满足重建条件的采用余弦调制结构的系统实现方法，并指出了其多项元素矩阵无损的充分必要条件，在精确重建的前提下，对低通原型滤波器系数进行了优化。     

Cancellation of aliasing in CCD low-pass filters

The spurious frequencies caused by aliasing in a CCD low-pass filter can be canceled in the passband by designing a prefilter into the CCDs input stage. In this paper, the authors describe how single- and multiple-stage prefilters can be used, the rejection band and attenuation being set by the number of stages. They describe the design of second-order and third-order prefilters. In a basic design, the filtering effect is obtained only around the odd multiples of clock frequency; in a more complex design, the filtering effect is also obtained around twice the clock frequency. A second-order prefilter has been integrated into the input stage of a CCD low-pass filter. Experimental results are presented.     

Subspace approach for the design of cosine-modulated filter bankswith linear-phase prototype filter

A method for designing perfect reconstruction (PR) prototypes for paraunitary cosine-modulated filter banks is presented. The design procedure is based on a subspace approach that allows linear combinations of even-length linear-phase PR prototype filters in such a way that the resulting filter is also a linear-phase PR prototype. Within a given subspace, the weights of the optimal linear combination can easily be computed via an eigenanalysis. The filter design is carried out iteratively while the PR property is guaranteed throughout the design process. No nonlinear optimization routine is needed. As a special case, the proposed approach allows the design of discrete-coefficient prototypes, which are of great interest for efficient hardware implementations     

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     

New compact ultra wideband bandpass filter using modified multi-mode resonator

A new compact ultra wideband (UWB) bandpass filter (BPF) using modified multi-mode resonator (MMR) is presented. The filter consists of a multi-mode resonator with dual spur-lines for providing the dual notch bands at 5.2 and 5.8 GHz and connected with a stepped impedance structure for controlling the transmission zeros at lower and higher passband edge. The interdigital coupling input/output (I/O) lines are used for coupling enhancement. The |S₂₁|-magnitude and the frequencies of notch bands can be well determined by tuning the dimensions of the dual spur-lines. The designed procedures are discussed and good agreement between the measurement and EM simulation are compared.     

Design of linear-phase IIR filters via impulse-response gramians

A new method for the design of a linear-phase infinite-impulse-response (IIR) filter is presented. It involves designing a finite-impulse-response (FIR) filter satisfying the given frequency response specifications and subsequently obtaining a significantly lower order IIR filter using model reduction based on impulse-response gramians. The general outline of the method and a brief overview of the existing linear-phase FIR filter design and model-reduction techniques are presented. The impulse-response gramian and the model-reduction algorithm used are presented. The method is illustrated by design examples and is compared with other methods for the design of linear-phase IIR filters using equalizers     

A novel approach for coefficient quantization of low-pass finite impulse response filter using differential evolution algorithm

Evolutionary computational techniques have been employed judiciously in various signal processing applications of late. In this paper, such an attempt has been made to design a low-pass linear-phase multiplier-less finite duration impulse response (FIR) filter using differential evolution (DE) algorithm. This particular evolutionary optimization technique has been explored to search the impulse response coefficients of the FIR filter in the form of sum of power of two (SPT) in order to avoid the multipliers during design process. The performance of the designed low-pass filter has been studied thoroughly in terms of its frequency characteristics and primitive requirement of fundamental hardware blocks. The superiority of our design has been ascertained over a number of existing techniques by various means. Finally, the proposed filter of different lengths has been implemented on a field programmable gate array (FPGA) chip for evaluating the competency of this work. The percentage improvement in hardware complexity produced by our design has also been computed and clearly listed in this paper for convenience.     

A new closed form method for design of variable bandwidth linear phase FIR filter using different polynomials

In this paper, a new method for the design of variable bandwidth linear-phase finite impulse response (FIR) filters using different polynomials such as shifted Chebyshev polynomials, Bernstein polynomials and shifted Legendre polynomials is proposed. For this purpose, the transfer function of a variable bandwidth filter, which is a linear combination of fixed-coefficient linear-phase filters and the above polynomials are separately exploited as tuning parameters to control bandwidth of the filter. In order to determine the filter coefficients, mean squared difference between the desired variable bandwidth filter and the practical filter is minimized by differentiating it with respect to its coefficients leading to a system of linear equations. The matrix elements can be expressed in form of Toeplitz-plus-Hankel matrix, which reduces the computational complexity. Several examples are included to demonstrate effectiveness of the proposed method in terms of passband error (e_p), stopband error (e_s) and stopband attenuation (A_s).     

Derivative-controlled design of linear-phase FIR filters via waveform moments

A new method for designing linear-phase finite impulse response (FIR) filters is proposed by using the blockwise waveform moments. The proposed method yields linear-phase FIR filters whose magnitude response and its derivatives to a certain order take the prescribed values at equally spaced frequency points. The design procedure only needs to solve a system of linear equations, whose size is slightly smaller than the degree of the resulting filter. In addition, the inversion of the linear equations can be essentially precomputed. Therefore, the proposed design method is computationally efficient. In particular, for some important cases, i.e., the maximally flat R-regular L/sup th/-band FIR filters, a closed-form formula can be obtained. It is also shown that the resulting R-regular L/sup th/-band FIR filters have the zero intersymbol interference property.     

全新布里渊散射可切换微波光子滤波器

提出了一个新的基于布里渊散射效应的微波光子滤波器。该滤波器可通过调谐系统中光滤波器的中心波长,实现高解析度带通滤波器与陷波滤波器之间的灵活切换,并且通过调谐产生受激布里渊散射的泵浦光的波长可实现滤波器通带或阻带的中心频率在很大频率范围内连续调谐。该滤波器为全光结构,因此具有非常大的调谐范围（调谐上限仅受限于试验中使用的矢量网络分析仪的显示频率上限）。系统中采用相位调制器,因此没有偏置电压漂移问题。实验结果展示了一个带通与陷波滤可灵活切换的高解析度微波光子滤波器,并且通带和阻带的中心频率在9～26.5 GHz范围内连续可调谐,其中带通滤波器的通带具有极窄3 dB带宽,约28 MHz（由光纤本身布里渊增益区线宽所决定）。     

New current–mode special function continuous-time active filters employing only OTAs and OPAMPs

This paper reports three current mode second order filters, each of which realizes a specific function without any external passive elements. These filters realize low-pass notch (LPN), high-pass notch (HPN) and all-pass (AP) functions. Two OPAMPs, a double output OTA and a single output OTA are employed for each circuit. The filter structures can be easily cascaded since they have high output impedances. This property is especially useful for achieving high-order filters using these LPN and HPN filters as building blocks. The presented theory is verified with macro models in SPICE simulations and, using the SPICE parameters of the layout technology, post layout simulations are carried out, with parasitics extracted from the layouts of the filter chips.