Class Of Low-pass Filters Research Articles

Signal Extraction for Nonstationary Time Series with Diverse Sampling Rules

Abstract This paper presents a flexible framework for signal extraction of time series measured as stock or flow at diverse sampling frequencies. Our approach allows for a coherent treatment of series across diverse sampling rules, a deeper understanding of the main properties of signal estimators and the role of measurement, and a straightforward method for signal estimation and interpolation for discrete observations. We set out the essential theoretical foundations, including a proof of the continuous-time Wiener-Kolmogorov formula generalized to nonstationary signal or noise. Based on these results, we derive a new class of low-pass filters that provide the basis for trend estimation of stock and flow time series. Further, we introduce a simple and accurate method for low-frequency signal estimation and interpolation in discrete samples, and examine its properties for simulated series. Illustrations are given on economic data.

Simulation of Fractional-Order Low-Pass Filters

The attenuation of standard analog low-pass filters corresponds to a multiple value of -6 decibels per octave. This quantified value is related to the order of the filter. The issue addressed here is concerned with the extension of integer orders to non integer orders, such that the attenuation of a low-pass filter can be continuously adjusted. Fractional differential systems are known to provide such asymptotic behaviors and many results about their simulation are available. But even for a fixed cutoff frequency, their combination does not generate an additive group with respect to the order and they involve stability problems. In this paper, a class of low-pass filters with orders between 0 (the filter is a unit gain) and 1 (standard one-pole filter) is defined to restore these properties. These infinite dimensional filters are not fractional differential but admit some well-posed representations into weighted integrals of standard one-pole filters. Based on this, finite dimensional approximations are proposed and recast into the framework of statespace representations-space representations. A special care is given to reduce the computational complexity, through the dimension of the state. In practice, this objective is reached for the complete family, without damaging the perceptive quality, with dimension 13. Then, an accurate low-cost digital version of this family is built in the time-domain. The accuracy of the digital filters is verified on the complete range of parameters (cutoff frequencies and fractional orders). Moreover, the stability is guaranteed, even for time-varying parameters. As an application, a plugin has been implemented which provides a new audio tool for tuning the cutoff frequency and the asymptotic slope in a continuous way. As a very special application, choosing a one-half order combined with a low cutoff frequency (20 Hz or less), the filter fed with a white noise provides a pink noise generator.

Low-pass filter design using locally weighted polynomial regression and discrete prolate spheroidal sequences

The paper concerns the design of nonparametric low-pass filters that have the property of reproducing a polynomial of a given degree. Two approaches are considered. The first is locally weighted polynomial regression (LWPR), which leads to linear filters depending on three parameters: the bandwidth, the order of the fitting polynomial, and the kernel. We find a remarkable linear (hyperbolic) relationship between the cut-off period (frequency) and the bandwidth, conditional on the choices of the order and the kernel, upon which we build the design of a low-pass filter. The second hinges on a generalization of the maximum concentration approach, leading to filters related to discrete prolate spheroidal sequences (DPSS). In particular, we propose a new class of low-pass filters that maximize the concentration over a specified frequency range, subject to polynomial reproducing constraints. The design of generalized DPSS filters depends on three parameters: the bandwidth, the polynomial order, and the concentration frequency. We discuss the properties of the corresponding filters in relation to the LWPR filters, and illustrate their use for the design of low-pass filters by investigating how the three parameters are related to the cut-off frequency.

A Gain Scheduled Sliding Mode Control Scheme Using Filtering Techniques With Applications to Multilink Robotic Manipulators

In this paper, a gain scheduled sliding mode control (SMC) scheme is proposed for tracking control tasks of multilink robotic manipulators. In the new scheme, filtering techniques play the key role in acquiring equivalent control signals and scheduling the switching control gain automatically. Once the system enters the sliding motion, two classes of low-pass filters are introduced to work concurrently for the purpose of acquiring equivalent control, reducing the switching gain effectively, and as a result eliminating chattering. By virtue of equivalent control theory, one class of filters is designed to capture the “average” profile of the switching quantity, which is in proportion to the desired control input. Meanwhile, another class of low-pass filters is added to scale down the gain of the switching control. The convergence property of the proposed control scheme is rigorously analyzed in time domain and the frequency domain knowledge can be easily incorporated into the construction of the two classes of filters. Excellent tracking performance is achieved with the direct manipulation of switching control input using filtering technology and with the integration of both time domain and frequency domain system knowledge in controller design. [S0022-0434(00)01604-X]

Design of filters with prescribed time response and Chebyshev stopband attenuation

This paper presents a new class of low pass filters with Chebyshev stopband attenuation which are intended for pulse applications and characterized by very small values of the dominant polo Q-factor, Their transfer functions are obtained by computational optimization in the time domain of either step response or impulse response under the constraint of double or higher-order multiplicity of the dominant pair of poles. The comparison with Schüssler filters, which are known for their excellent rise-time-overshoot characteristics, reveals that the new filters yield superior frequency and time domain characteristics and yet they have much smaller values of the dominant pole Q-factor. The pole locations and other important frequency and time-domain parameters are tabulated for optimum step response and for optimum impulse response for n = 5, 6, 7, 8 and several values of the maximum tolerable overshoot.

All-pole filter designs using lagrangian multipliers

Abstract New classes of low-pass filters with no finite zeros and having a non-monotonic passband are introduced. This is achieved by minimizing the least-mean-square error in the passband with respect to a weighting function. These filters can be obtained using two different analytic techniques. Many conventional filters are derived as special cases of this approximation. Using different weighting functions numerous filter responses can be obtained.

Transitional Murromaf–Murroer filters

A new class of lowpass filters with all transmission zeros at infinity, having equal-ripple behaviour in the passband, is described. The transfer function of these filters, referred to as transitional Murromaf-Murroer filters, is obtained by adding the multiple real poles and reducing the number of complex pole pairs to realise a lowpass RC active filter with a reduced number of amplifiers with respect to the classical transitional Butterworth-Chebyshev filters.

Time-domain synthesis of transfer functions for low sensitivity active filters

This paper presents a new class of lowpass filters with all transmission zeros at infinity which are intended for pulse applications. Their transfer functions are derived by computational optimization in the time domain of either step response or impulse response under the constraint of double or higher-order multiplicity of the dominant pair of poles. The frequency and time-domain characteristics of these filters compare favourably with these for Schussler filters which are known for their superior rise-time overshoot relationship. Yet, due to the multiplicity of the dominant pair of poles, the critical pole Q factor is very much decreased. Thus, the new filter functions can be advantageously applied in the synthesis of low sensitivity networks and particularly in the design of low sensitivity active filters. The pole locations and some other important frequency and time-domain parameters are tabulated for optimum step response and for optimum impulse response for nequals; 5-9 and several values of the m...

Modified Butterworth filters†

A novel class of low-pass filters with zero pass-band loss at the origin and at the fixed frequency near the band-edge and satisfying (n − 2) magnitude flatness conditions at the latter are described. The magnitude characteristics of these filters are superior to those for the Butterworth filters and some other recently introduced classes of low-pass filters. They also compare favourably with Legendre monotonic pass-band filters. The all-pole filter functions of this type are discussed as well as the filter function with finite real frequency transmission zeros exhibiting Chebyshev stop-band attenuation characteristics.

Generalized analysis of optimum monotonic low-pass filters

New classes of low-pass filters with no finite zeros having a monotonic passband response are introduced by maximizing or minimizing the mean square error and changing the boundaries of the error integral. It is shown that all known classes of filters with monotonic passband magnitude response (Butterworth, Legendre, LSM, and Halpern filters) are obtained as special cases of this type of approximation.

Lowpass filter with minimum integrated power-loss ratio in the passband

A class of lowpass filters with minimum integrated power-loss ratio in the passband is discussed. Comparisons with the usual Butterworth and Cheby-shev filters are also reported.

Transitional Halpern-Thomson filters

A new class of lowpass filter, with all transmission zeros at infinity, having a monotonic passband response is described. The transfer function of these filters, referred to as transitional Halpern-Thomson (t.h.t.) filters, depends on a variable parameter that enables a tradeoff between, the overshoot and the risetime in response to a unit-step input.

A new class of filters for pulse applications

Abstract This paper presents the results of an investigation on the steady-state and transient response characteristics of a new class of low-pass filters. The natural frequencies of the proposed filters all lie on catenary contours and the transmission zeros are all at infinity. This class of ladder filters has some useful transmission properties when both time and frequency domain considerations are important. The response characteristics of this class of filters are compared with, those of the Butterworth and Thomson filters and the recent class of filters due to Mullick. We show that this class has some advantages when the rise-time, overshoot, and 3db frequency of the magnitude response (with no frequency peaking) are all of importance simultaneously.