Inverse Chebyshev Filters Research Articles

Designing of CCII-Based Fractional Order Inverse Chebyshev Filters Using Gray Wolf Optimization Approach

The paper introduces a new approach for designing fractional-order inverse Chebyshev low-pass filters (FOICLF), with an emphasis on filters with an order of 1+α. The coefficients for these filters are determined through Gray Wolf Optimization by approximating filter response with the ideal response of same order FOICLF. Stability tests are conducted, and filters are implemented using Multiple Input Single Output topology with commercial ICs. Comparative analysis reveals close proximity between the ideal response of FOICLF and the designed filters, featuring maximum and mean square errors of –22.48 dB and –61.07 dB, respectively, for 1.7 order. Results are benchmarked against existing literature, highlighting superior performance in stopband and passband magnitude errors and stopband attenuation. Process, Voltage, and Temperature analysis assesses the impact of the parameter variations on the –3 dB frequency, assuring the robustness of designed filters with relative standard deviations ranging from 0.003% to 3.013% for the 1.7 order filter.

Wideband 1-Bit Bandpass Delta Sigma Modulator Using Elliptic Filter in Noise Transfer Function

A 1-bit band-pass delta-sigma modulator (BP-DSM), which utilizes oversampling technology, allows a modulated signal to be directly output by using a high-speed 1-bit digital pulse train, thus realizing miniaturization of transmitters. For 1-bit BP-DSM, the noise transfer function (NTF) is used to suppress quantization noise power in the transmission band and a guideline of out-of-band gain of |NTF|< 1.5 is used to prevent oscillation. However, in previous studies, such as Butterworth and inverse Chebyshev filters, the out-of-band gain was designed indirectly by tuning the zeros and poles in the transmission band and thus, was not stabilized sufficiently. Furthermore, even though the zeros of the NTF are identical to the poles of the loop filter, there are still widely used designs in which the zeros are set on the unit circle, making stabilization quite difficult. Therefore, in this paper, we propose a feasible implementation of the NTF for 1-bit BP-DSM with an elliptic filter that can be used to set not only in-band but also out-of-band gain, in which both the zeros and poles are set inside the unit circle. As a design result, a modulation bandwidth of 400 MHz as a relative bandwidth of 11%, a noise suppression bandwidth of 800 MHz, and an adjacent channel leakage power ratio of 50 dB were achieved at a center frequency of 3.6 GHz, enabling a wider bandwidth and higher SNR than before by improving the stability.

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.

Inverse general Chebyshev bandpass filters

SummaryIn this paper, the synthesis of inverse general Chebyshev bandpass filters is discussed. Unlike general Chebyshev filters that flexibly place transmission zeros to mainly control the performance of the filters in the stopband and keep constant ripple in the passband, inverse general Chebyshev filters are featured by flexible placement of reflection zeros in the passband and keep constant ripple in the stopband. Two approaches to directly derive filtering polynomials of inverse general Chebyshev bandpass filters in the bandpass domain are discussed in detail. By applying the zero‐extraction method, these filtering polynomials could be realized through appropriate networks. Finally, two examples are presented for demonstration.

Performance analysis of WDM-PON architecture using different receiver filters

In this paper the performance effect of a 40Gb/s Wavelength-Division-Multiplexed Passive Optical Network (WDM-PON) is analyzed using different receiver filters namely Integrator filter, Bessel filter, Butterworth filter, Chebyshev filter, Inverse Chebyshev filter, Elliptic filter, Gaussian filter and Rectangular filter. The data rate and channel spacing are taken as 10Gb/s per channel and 100GHz, respectively. Among all the investigated filters, Bessel filter is considered to be the best one for WDM-PON network by the obtained BER and Q factor values.

A High Performance & Efficiently Designed IIR Filter Using Graphical Virtual Tool (LabVIEW)

Designing of digital filters based on LABVIEW involves the concept of virtual instrumentation. In the recent years LABVIEW finds many applications in different fields for example industrial purpose like level sensor, temperature sensor pressure sensor etc. Virtual instruments are used in LABVIEW. Each VI has three parts a block diagram, a front panel and a connector panel. Connector panel is used to represent the VI in the block diagrams of other. Controls and indicators on the front panel allow an operator to input data into or extract data from a running virtual instrument. The front panel can also serve as a programmatic interface. A digital IIR filter system is developed using LABVIEW software. IIR filters possess certain properties which makes them preferred design choices in many situations over FIR filters. Following are the types of IIR filter Butterworth filters, Chebyshev filters, Inverse chebyshev filters, Elliptic filters. Virtual instrument reads the desired parameters of the filters entered by the user on the front panel and determines its magnitude response

UHF Receiver Front-End: Implementation and Analog Baseband Design Considerations

An integrated ultrahigh-frequency (UHF) receiver is presented. A systematic analysis to quantify the interdependence of baseband filter and analog-to-digital converter (ADC) dynamic range in broadband receivers is presented. This analysis shows that: (1) low-order Butterworth filters are favorable when undesired power is dominated by far out blockers and (2) high-order inverse Chebyshev filters can reduce the resolution of a subsequent ADC by up to two additional bits in the presence of adjacent analog narrowband blockers. Based on the analysis, a cascaded, programmable, hybrid active-RC and switched-capacitor (SC) baseband filter is proposed. An all-digital nonoverlap clock tuning system to minimize the variation of available settling time window in SC circuits is also proposed. The receiver integrates the proposed filter with an RF variable gain amplifier (RFVGA) and a passive mixer. This receiver achieves a measured noise figure of 7.9 dB, an IIP3 of -8 dBm at maximum gain and +2 dBm at 9-dB RF attenuation. The chip consumes 120 mW (RFVGA, mixer and I-channel baseband) from 1.8-V analog/2.5-V digital dual supply and occupies 2.14 mm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> in IBM 0.18-μm RF CMOS technology.

Analysis of Digital IIR Filter with LabVIEW

Aiming at importance of virtual instruments in the field of Digital Signal Processing, a digital IIR Filter system is developed using National Instruments (NI) data LabVIEW software package. All the types of IIR filters like Butterworth filters, Chebyshev filters, inverse Chebyshev filters, and Elliptic filters are designed to generate their magnitude response and filter coefficients. The LabVIEW software is used to develop virtual instrument (VI) that includes a front panel and a functional diagram. The VI reads the desired parameters of the filters entered by the user on the front panel and determines its magnitude response and filter coefficients.

류마티스 관절염 환자의 무릎 MR 영상 개선을 위한 변형된 Fermi 필터 설계

In this study, we intended to design the optimal Fermi filter to apply the k-space date that is knee image of the rheumatoid arthritis patient acquired from the MRI (magnetic resonance imaging) instrument. After deciding the suitable coefficient for the Fermi filter, the results were compared with modified Fermi filter and inverse Chebyshev filter, Chebyshev filter, Elliptic filter and Butterworth filter. Firstly, in comparison to the results, the radiologist confirmed that modified Fermi filter was best decision for boundary of the rheumatoid arthritis images. The number of the black voxels of the histogram showed the quantity of the results. At the proposed filter images, numbers of the blacks voxels were statistically decreased. That meant voxels only appeared the black color were changed to others voxels color. Because the number of the total voxels was fixed, the area appeared block color could be effected to the other areas. If the modified Fermi filter were used for rheumatoid arthritis patient, the result will be better than other filters.

Modified Chebyshev lowpass filters

AbstractSimple modifications are proposed for the normal as well as the inverse Chebyshev filter (ICF) for facilitating doubly terminated LC ladder realization, and consequently cascaded active‐RC implementations, for all specifications. The resulting filters are compared with two recently proposed solutions, as well as the competing conventional ones in terms of cutoff slope and the Q of the complex poles. The advantages of the modified filters are discussed. Copyright © 2009 John Wiley &amp; Sons, Ltd.

Inverse Ultraspherical Filters

The inverse ultraspherical filter is derived and its properties analyzed. It is shown that the inverse ultraspherical filter has smaller transition band than the inverse Chebyshev filter under certain circumstances while still maintaining the maximally flat passband characteristic. Filter pole and zero calculations are described and typical magnitude and delay responses generated. Nomographs of inverse ultraspherical filters are also provided for determining filter order and for possible magnitude response optimization.

Direct design of Chebyshev-type recursive digital filters

A method for the design of Chebyshev infinite impulse response (IIR) digital filters directly in the digital domain is given. This approach is easier to use than the bi-linear transformation, does not require pre-warping, and provides (in virtually all cases of practical interest) filters with significantly improved roll-off rates for comparable hardware cost. The extension to inverse-Chebyshev filters is also given.

Improved version of the inverse Chebyshev filter

The inverse Chebyshev function is formed by a transformation of a rational equiripple function defined by two polynomial Chebyshev functions of the same order. Since the transformation moves the finite complex zeros of the original rational function to the imaginary axis, its main imperfections, such as low selectivity and relatively large Q factors of the zeros, are eliminated. Extremely low pole-Q factors of the initial function are retained, providing a low sensitivity and a good group delay.

Explicit formulas for lattice wave digital filters

Explicit formulas are derived for designing lattice wave digital filters of the most common filter types, for Butterworth, Chebyshev, inverse Chebyshev, and Cauer parameter (elliptic) filter responses. Using these formulas a direct top down design method is obtained and most of the practical design problems can be solved without special knowledge of filter synthesis methods. Since the formulas are simple enough also in the case of elliptic filters, the design process is sufficiently simple to serve as basis in the first part (filter design from specs to algorithm) of silicon compilers or applied to high level programmable digital signal processors.

Transitional rational filters

Transitional rational XY filters (TRXY) with rational transfer functions are considered having characteristics that vary smoothly from those of filter X to those of filter Y as certain parameters are varied continuously. The X and Y filters are chosen as various combinations of the ultraspherical rational filter, the generalized Bessel rational filter and the inverse Chebyshev filter.

Maximally Flat Amplitude Low-Pass Filter with an Arbitrary Number of Pairs of Real Frequency Transmission Zeros

The synthesis of a general class of filter with maximally flat passband and Chebyshev stopband attenuation characteristic is presented. The filter has an nth order voltage transfer function with m pairs of transmission zeros in the stopband, where <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n \geq 2 m + 1</tex> . Butterworth and inverse Chebyshev filters are special cases of this general class with <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m = 0</tex> and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n = 2m + 1</tex> , respectively.

Attenuation Characteristics and Realization of Odd-Order Generalized Inverse Chebyshev Filters

Tables of transition bandwidth ratio, zero transmission and minimum attenuation frequencies in the stopband, and element values for two kinds of realizations of odd-order generalized inverse Chebyshev filters with <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</tex> up to 11 and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</tex> up to 3, all using minimum stopband loss as a parameter, are given.