Minimum Stopband Attenuation Research Articles

Universal Graph Filter Design Based on Butterworth, Chebyshev, and Elliptic Functions

Graph filters are crucial tools in processing the spectrum of graph signals. In this paper, we propose to design universal IIR graph filters with low computational complexity by using three kinds of functions, which are Butterworth, Chebyshev, and elliptic functions, respectively. Specifically, inspired by the classical analog filter design method, we first derive the zeros and poles of graph frequency responses. With these zeros and poles, we construct the conjugate graph filters to design the Butterworth high-pass graph filter, Chebyshev high-pass graph filter, and elliptic high-pass graph filter, respectively. On this basis, we further propose to construct a desired graph filter of low pass, band pass, and band stop by mapping the parameters of the desired graph filter to those of the equivalent high-pass graph filter. Furthermore, we propose to set the graph filter order given the maximum passband attenuation and the minimum stopband attenuation. Our numerical results show that the proposed graph filter design methods realize the desired frequency response more accurately than the autoregressive moving average graph filter design method, the linear least-squares fitting-based graph filter design method, and the Chebyshev FIR polynomial graph filter design method.

Area- and Power-Efficient Nearly-Linear Phase Response IIR Filter by Iterative Convex Optimization

Low complexity infinite impulse response (IIR) filter design with nearly-linear phase response has attracted considerable attention in recent years due to the substantially high area and power consumption of linear phase finite impulse response (FIR) filter. Compared with the FIR filter, designing an IIR filter with the minimized group delay deviation and low power cost is a challenging topic. In this paper, the non-convex group delay deviation minimization problem for IIR filter design is reformulated into an iterative optimization problem to achieve lower group delay deviation. The hardware complexity of the solution is iteratively reduced by approximating the IIR filter coefficients to maximize the number of eliminable common subexpressions. The headroom for the coefficient adjustment is governed by the gradient of group delay deviation between iterations. Using our proposed design algorithm, a high-order lowpass filter with a minimum stopband attenuation of 60dB can be implemented by a 13-tap IIR filter with a group delay deviation of 0.002 only, as opposed to two linear-phase FIR filters designed by two recent and competitive FIR filter design algorithms with tap number of 51 and 57, respectively. Logic synthesis shows that the proposed IIR design saves 39.4% of the area and 41.8% of power consumption over the FIR solutions. Comparing with the latest nearly-linear phase IIR filter design algorithms, the group delay deviation of the solutions generated by our proposed algorithm are on average 25.5% lower, along with an average area and power savings of 20.5% and 18.4%, respectively, from the logic synthesis results.

Analysis of PC6 window function using fractional Fourier transform

Fractional Fourier transform (FRFT) is a linear transform generalizing Fourier transform (FT) that plays an important role in the field of signal processing and analysis. FRFT contains an adjustable parameter α, which it rotates the signal in the time frequency plane and represents the signal in an intermediate domain between time and frequency. FRFT provides a measure about the angular distribution of signal's energy in time frequency plane. FT is a special case of FRFT when angle α is equal to π/2. This paper presents mathematical model for obtaining FRFT of PC6 window function. The different parameters of this window function are also obtained with the help of simulation results. A comparison of window function parameters is presented using FT and FRFT. Also comparison of this window function with Hanning window function is presented in terms of Side Lobe Fall off Rate (SLFOR). For different values of FRFT order, PC6 window function shows variation in different parameters. Thus by changing the FRFT order, the minimum stop band attenuation of the resulting window function can be controlled.

Design of optimal high pass and band stop FIR filters using adaptive Cuckoo search algorithm

This paper presents an efficient design of digital FIR high pass and band stop filters using an adaptive cuckoo search algorithm (ACSA). The important features of ACSA are — (i) the step size is independent and (ii) it is accurately decided from the current fitness value. The step size is decided according to the current fitness value within the iteration process. This increases the convergence speed. The other five global optimizers are also used for optimization. The optimal solutions obtained by the ACSA are compared with the other global optimizers. CEC 2005 benchmark test functions are considered for the comparison. The results are compared in terms of the convergence speed, accuracy, deviation from the desired response, minimum stop-band attenuation and maximum pass-band attenuation. The statistical analysis, i.e. t-Test is performed to claim the superiority of the proposed approach. The simulation results presented in this paper reveal the fact that the performance of the ACSA is better than the other algorithms.

Kaiser ve Von-Hann Pencereleri Tabanlı Yeni bir Pencere Fonksiyonu ve Onun Sayısal Süzgeç tasarımındaki Performans Analizi

Digital filters, which are used in many signal processing applications, can be classified as recursive or nonrecursive. Since nonrecursive digital filters can provide inherent stability and exact linear phase characteristic, they have an important place in the literature. In this paper, a new hybrid function is proposed for the design of nonrecursive digital filters. This new window was obtained by combining two different window functions known as Kaiser and Von-Hann in the literature. First of all, the effects of two independent parameters of the proposed window function on the digital filter characteristic are analysed in terms of minimum stopband attenuation and transition bandwidth. Later, comparative examples for different filter lengths are given to compare the performance of the proposed window function in the design of digital filter with the well-known other two parameter window functions. Simulation results demonstrate that the proposed window function can provide a better filter design than Kaiser-Hamming, Saramaki, Kaiser, Dolph-Chebychev, Cosh, Exponential, and Gaussian window functions.

NEW TYPE OF NEARLY MONOTONIC PASSBAND FILTERS WITH SHARP CUTOFF

New type of nearly monotonic rational function with one pair of zeros on imaginary axis has been proposed. By using these new functions with zeros as a parameter, it is possible to make tradeoff between minimum stopband attenuation and selectivity of the amplitude characteristic. In order to present efficiency of the proposed filter, comparison with allpole filter monotonic in the passband and inverse Chebyshev filter is presented. Also, design example for the seventh order new type lowpass filter is given.

Optimal Design of 2D FIR Filters with Quadrantally Symmetric Properties Using Fractional Derivative Constraints

In this article, an optimal design of two-dimensional finite impulse response (2D FIR) filter with quadrantally even symmetric impulse response using fractional derivative constraints (FDCs) is presented. Firstly, design problem of 2D FIR filter is formulated as an optimization problem. Then, FDCs are imposed over the integral absolute error for designing of the quadrantally even symmetric impulse response filter. The optimized FDCs are applied over the prescribed frequency points. Next, the optimized filter impulse response coefficients are computed using a hybrid optimization technique, called hybrid particle swarm optimization and gravitational search algorithm (HPSO-GSA). Further, FDC values are also optimized such that flat passband and stopband frequency response is achieved and the absolute $$L_1$$L1-error is minimized. Finally, four design examples of 2D low-pass, high-pass, band-pass and band-stop filters are demonstrated to justify the design accuracy in terms of passband error, stopband error, maximum passband ripple, minimum stopband attenuation and execution time. Simulation results have been compared with the other optimization algorithms, such as real-coded genetic algorithm, particle swarm optimization and gravitational search algorithm. It is observed that HPSO-GSA gives improved results for 2D FIR-FDC filter design problem. In comparison with other existing techniques of 2D FIR filter design, the proposed method shows improved design accuracy and flexibility with varying values of FDCs.

Simulation Based Design Analysis of an Adjustable Window Function

Window based Finite Impulse Response filters have the problem that in order to obtain better performance from these filters in terms of minimum stopband attenuation cost has to be paid for half main-lobe width and vice-versa. A solution of this contradictory behavior is to increase the length of the window which in turn requires more hardware hence increasing the cost of system. This paper proposes a novel window based on two shifted hyperbolic tangent functions. The proposed window contains an adjustable parameter, with the help of which desired time and frequency domain characteristics may be achieved for relatively shorter window length. The characteristics of the proposed window are compared with those of the two well-known adjustable windows namely Cosh window and Exponential window. MATLAB simulation results show that for the same value of window length, the proposed window provides improved output, and thus it makes a good compromise between minimum stopband attenuation and half main-lobe width compared to the windows mentioned previously.

Design of fir filters using exponential--Hamming window family

In this paper, a new two-parameter window obtained by the combination of two windows, known as exponential and Hamming, is proposed and applied for the design of finite impulse response (FIR) digital filters. First of all, the quality of the proposed window is analyzed in terms of window spectral parameters and then compared with other two-parameter windows, namely Kaiser, cosh, and exponential. The window simulation results show that the proposed window can provide better ripple ratio than other windows for fixed window length and mainlobe width. Secondly, the performance of the proposed window is analyzed in digital filter design. The filter numerical comparison with Saramaki, Kaiser, Dolph–Chebyshev, cosh, and exponential windows confirms that the filter designed by the proposed window can exhibit a better filtering performance compared to well-known two-parameter windows in the literature because it can provide better minimum stopband attenuation for fixed filter length and transition width.

Design of minimax robust broadband beamformers with optimized microphone positions

A new method for the design of robust minimax far-field broadband beamformers with optimized microphone positions is proposed. The method is formulated as an iterative optimization problem where the maximum passband1 magnitude response error is minimized and the microphone positions are optimized while ensuring that the minimum stopband attenuation is above a prescribed level. To maintain robustness, we constrain a sensitivity parameter, namely, the white noise gain, to be above prescribed levels across the frequency band. An additional feature of the method, which is quite useful in certain applications, is that it provides the capability of constraining the gain in the transition band to always lie below the maximum gain in the passband. Performance comparisons with existing methods show that the optimization of the microphone positions results in beamformers with superior performance.

L -infinity norm design of linear-phase robust broadband beamformers using constrained optimization

A new method for the design of linear-phase robust far-field broadband beamformers using constrained optimization is proposed. In the method, the maximum passband ripple and minimum stopband attenuation are ensured to be within prescribed levels, while at the same time maintaining a good linear-phase characteristic at a prescribed group delay in the passband. Since the beamformer is intended primarily for small-sized microphone arrays where the microphone spacing is small relative to the wavelength at low frequencies, the beamformer can become highly sensitive to spatial white noise and array imperfections if a direct minimization of the error is performed. Therefore, to limit the sensitivity of the beamformer the optimization is carried out by constraining a sensitivity parameter, namely, the white noise gain (WNG) to be above prescribed levels across the frequency band. Two novel design variants have been developed. The first variant is formulated as a convex optimization problem where the maximum error in the passband is minimized, while the second variant is formulated as an iterative optimization problem and has the advantage of significantly improving the linear-phase characteristics of the beamformer under any prescribed group delay or linear-array configuration. In the second variant, the passband group-delay deviation is minimized while ensuring that the maximum passband ripple and stopband attenuation are within prescribed levels. To reduce the computational effort in carrying out the optimization, a nonuniform variable sampling approach over the frequency and angular dimensions is used to compute the required parameters. Experiment results show that beamformers designed using the proposed methods have much smaller passband group-delay deviation for similar passband ripple and stopband attenuation than a modified version of an existing method.

A 4th-order Switch-capacitor Low-pass Filter for Quartz Gyroscope Interface Circuit

This paper presents the computer aided design of a 4th-order switch-capacitor low-pass filter applied in quartz gyroscope interface circuit. After a introduction of switch-capacitor filter (SCF) and its application in quartz gyroscope, the system-level analysis and design is given. Then the circuit design of amplifier, CMOS switch and non-overlapping clock is described. The Fourth-order low-pass SCF has been implemented under 0.5um CMOS process and simulated in computer aided design software. The final simulation results show that the passband is 99.7Hz , and the maximum pass-band ripple is about 0.14dB.The stop-band is 1KHz, and the minimum stop-band attenuation is 78.6dB. DOI: http://dx.doi.org/10.11591/telkomnika.v11i10.3398

Performance Of Modified Cosh Window Function

In this paper, we have analyzed the performance of modified Cosh window function.A new parameter has been proposed to the previous 2-parameter Cosh window to improve its spectral characteristics in terms of ripple-ratio and transition width.It is observed by several iterations that by increasing the values of new parameter so proposed there is a significant variation in ripple ratio and transition width of the window spectrum.By the suitable combination of two parameters of the proposed window function, an optimum modified Cosh window is derived for N=51 and N=101.Optimum window provides better spectral characteristics. This modified window has applications in digital FIR designing, image processing as it provides better minimum stop band attenuation and contrast ratio respectively.An example has been taken to show the better performance of the proposed window for FIR filter designing for specified requirements.

Design and Simulation of Switched Capacitor Filter for Speed Change Parameter Converter

In this paper, we design a high-order switched capacitor filter for rapid change parameter converter. This design uses a structure which consists of three biquads filter sub-units. The design is a 6th-order SC elliptic low-pass filter, and the sample frequency is 250 kHz. By the MATLAB Simulink simulation, the system can meet the design requirements in the time domain. In this paper, the 6th-order switched capacitor elliptic low-pass filter was implemented under 0.5 um CMOS process and simulated in Cadence. The final simulation results show that the pass-band cutoff frequency is 10 kHz, and the maximum pass-band ripple is about 0.106 dB. The stop-band cutoff frequency is 20 kHz, and the minimum stop-band attenuation is 74.78 dB.

Comparison of Various Window Functions Used in FIR Filter Designing

In this study, 2-parameter cosh window is modified to improve its spectral characteristic in terms of the ripple ratio by proposing a new additional parameter. It is observed that an increase in the new parameter results in wider mainlobe width and smaller ripple ratio. By choosing the suitable combinations of the two adjustable parameters for the proposed modified window, the optimum windows that yield the minimum ripple ratio for N=51 and N=101 are .found. Simulation results show that the filters designed by proposed 3-parameter Cosh window provide higher quality in terms of the minimum stop-band attenuation for a fixed order, and yield lower order for a fix minimum stop-band attenuation compared to the filters designed by other windows.

COMPARATIVE ANALYSIS OF EXPONENTIAL WINDOW FUNCTION FOR DESIGNING OF FIR FILTERS

Filters are very commonly found in everyday life and include examples such as water filters for water purification, mosquito nets that filter out bugs, bouncers at bars filtering the incoming guests according to age (and other criteria), and air filters found in air conditioners that we are sometimes a bit too lazy to change/clean periodically. Filters have two uses: signal separation and signal restoration. Signal separation is needed when a signal has been contaminated with interference, noise, or other signals. For example, imagine a device for measuring the electrical activity of a baby's heart (EKG) while still in the womb. The raw signal will likely be corrupted by the breathing and heartbeat of the mother. A filter might be used to separate these signals so that they can be individually analyzed. Signal restoration is used when a signal has been distorted in some way. For example, an audio recording made with poor equipment may be filtered to better represent the sound as it actually occurred [1, 2]. The main goal of this work is to study the exponential  window function and analyze a digital low pass FIR filter using the same in MATLAB. Properties of window functions is studied and frequeny domain responses of window functions is obtained. Then FIR filter is designed using widow design method and its characteristics have also been studied in frequency domain. The performace comparison between LPFs designed using other well known windows like Kaiser, Exponential, Cosh and modified kaiser window is done and it has been intuitively shown that for a given order and transition width, the filter designed using Exponential window provides the worse minimum stop band attenuation but better far end attenuation than filter designed by well known Kaiser Window.

Efficient Multirate EMQF Digital Filters

This work gives an original method that combines multirate technique and the most efficient elliptic filter of low order to implement sharp digital filters with minimum stopband attenuation from 10 do 100 dB, but with vary small pass-band ripple. The theory and the design procedure are presented in software Mathematica. Ill. 10, bibl. 11, tabl. 1 (in English; abstracts in English and Lithuanian).DOI: http://dx.doi.org/10.5755/j01.eee.119.3.1360

Analysis of Dirichlet, Generalized Hamming and Triangular window functions in the linear canonical transform domain

Linear canonical transform is a four-parameter class of integral transform that plays an important role in many fields of optics and signal processing. Well-known transforms such as the Fourier transform, the fractional Fourier transform, and the Fresnel transform can be seen as the special cases of the linear canonical transform. This paper presents a new mathematical model for obtaining the linear canonical transforms of Dirichlet, Generalized “Hamming”, and Triangular window functions. The different window function parameters are also obtained from the simulations. By changing the value of four parameters and then changing the adjustable parameter, the main-lobe width, −3 dB bandwidth, −6 dB bandwidth and correspondingly, the minimum stop-band attenuation of the resulting window functions can be controlled. It has been shown that by using linear canonical transform, we are able to obtain all window parameters successfully as compared to fractional Fourier transform.

Analysis of Dirichlet and Generalized “Hamming” window functions in the fractional Fourier transform domains

A new mathematical model for obtaining the fractional Fourier transforms of Dirichlet and Generalized “Hamming” window functions is presented. The different parameters for the window functions are also obtained with the help of simulations. The fractional Fourier transformation contains an adjustable parameter with which the main lobe width and correspondingly, the minimum stop band attenuation of the resulting window function can be controlled.

A Methodology for Rapid Prototyping Peak-Constrained Least-Squares Bit-Serial Finite Impulse Response Filters in FPGAs

Area-efficient peak-constrained least-squares (PCLS) bit-serial finite impulse response (FIR) filter implementations can be rapidly prototyped in field programmable gate arrays (FPGA) with the methodology presented in this paper. Faster generation of the FPGA configuration bitstream is possible with a new application-specific mapping and placement method that uses JBits to avoid conventional general-purpose mapping and placement tools. JBits is a set of Java classes that provide an interface into the Xilinx Virtex FPGA configuration bitstream, allowing the user to generate new configuration bitstreams. PCLS coefficient generation allows passband-to-stopband energy ratio (PSR) performance to be traded for a reduction in the filter's hardware cost without altering the minimum stopband attenuation. Fixed-point coefficients that meet the frequency response and hardware cost specifications can be generated with the PCLS method. It is not possible to meet these specifications solely by the quantization of floating-point coefficients generated in other methods.