scholarly journals Convolution Integral: How a Graphical Type of Solution Can Help Minimize Misconceptions

2021 ◽  
Vol 3 (2) ◽  
pp. 103
Author(s):  
Hendra J. Tarigan
Keyword(s):  
Impulse Response ◽  
Physical System ◽  
Convolution Integral ◽  
Pass Filter ◽  
Low Pass Filter ◽  
Convolution Integrals ◽  
Low Pass ◽  
Simulation And Experiment ◽  
Rc Circuit ◽  
Set Up

A physical system, Low Pass Filter (LPF) RC Circuit, which serves as an impulse response and a square wave input signal are utilized to derive the continuous time convolution (convolution integrals). How to set up the limits of integration correctly and how the excitation source convolves with the impulse response are explained using a graphical type of solution. This in turn, help minimize the students’ misconceptions about the convolution integral. Further, the effect of varying the circuit elements on the shape of the convolution output plot is presented allowing students to see the connection between a convolution integral and a physical system. PSpice simulation and experiment results are incorporated and are compared with those of the analytical solution associated with the convolution integral.

scholarly journals Adaptive anti-disturbance control for a class of unknown pure feedback switched nonlinear systems

2021 ◽  
Author(s):  
Longsheng Chen
Keyword(s):  
Nonlinear Systems ◽  
Design Method ◽  
Tracking Error ◽  
Average Dwell Time ◽  
Switched Nonlinear Systems ◽  
Pass Filter ◽  
Low Pass Filter ◽  
Control Scheme ◽  
Low Pass ◽  
Set Up

Abstract In this study, an adaptive anti-disturbance control scheme is investigated for a class of unknown pure feedback switched nonlinear systems subjected to immeasurable states and external disturbances. Radial basis function neural networks (RBFNNs) are employed to identify the switched unknown nonlinearities, and a Butterworth low-pass filter is adopted to remove the algebraic loop problem. Subsequently, a novel switched neural state observer and a novel switched disturbance are presented via the coupled design method to estimate the immeasurable states and compounded disturbances. Then, an improved adaptive control strategy for the studied problem is designed with the help of a filtering method to eliminate the “explosion of complexity” problem, and certain compensating signals are set up to compensate for the filter errors, where switched updated laws are constructed to lessen the conservativeness caused by adoption of a common updated law for all subsystems. By utilizing the Lyapunov stability theorem, the developed control scheme can guarantee that all signals in the closed-loop system are bounded under a class of switching signals with the average dwell time (ADT), while the tracking error can converge to a small neighbourhood of origin. Finally, simulation results are provided to demonstrate the effectiveness of the presented approach.

Near‐real time reduction of shipboard gravity using Kalman‐filtered GPS measurements

Geophysics ◽  
1991 ◽  
Vol 56 (12) ◽  
pp. 1971-1979 ◽  
Author(s):  
J. F. Genrich ◽  
J.-B. Minster
Keyword(s):  
Real Time ◽  
Impulse Response ◽  
Finite Impulse Response ◽  
Yield Data ◽  
Pass Filter ◽  
Low Pass Filter ◽  
Marine Gravity ◽  
Gravity Measurements ◽  
Low Pass ◽  
Stabilized Platform

We have developed a Kalman filter to estimate accurate Eötvös corrections and horizontal ship accelerations from Global Positioning System (GPS) fixes. High‐resolution shipboard gravity measurements are obtained with a newly designed, linear phase, Finite Impulse Response (FIR) low‐pass filter. Both filters are combined to yield accurate, near‐real time, Eötvös‐corrected underway gravity estimates. Error ranges that reflect uncertainty in navigation for these estimates are calculated from autocovariances of Kalman velocity estimates by means of variance propagation expressions for time‐invariant linear digital filters. Estimates of horizontal ship acceleration are combined with a simplified instrument impulse response model in an attempt to remove transient noise from the gravimeter output. We apply the technique to data collected by two shipboard gravimeters, a LaCoste & Romberg Model S Air‐Sea Gravity Meter and a Bell Aerospace BGM-3 Marine Gravity Meter System, operated side‐by‐side on the Scripps R/V Thomas Washington during Leg 1 of the Roundabout expedition. In the absence of significant horizontal accelerations due to course or speed changes, both instruments yield data with good repeatability, characterized by rms differences of less than 1 mGal. Horizontal accelerations generate transient signals that cannot be modeled at present to an accuracy of better than 5 mGal. Difficulties in removing these transients are primarily due to insufficient quantitative knowledge of the response of the instrument, including the gyro‐stabilized platform. This can be determined analytically or empirically.

Research on the Short-Time Bias Stability of the Solid Vibration Beam Gyroscope

2011 ◽  
Vol 179-180 ◽  
pp. 86-91
Author(s):  
Xian Lin Bai ◽  
Yong Le Lu ◽  
Yu Liu
Keyword(s):  
Solid State ◽  
Output Signal ◽  
Transient Solution ◽  
Short Term ◽  
Pass Filter ◽  
Low Pass Filter ◽  
Bias Stability ◽  
Low Pass ◽  
Simulation And Experiment ◽  
Short Time

In this paper, Short-term bias stability of solid state vibration beam gyroscope is studied. Based on the dynamical equation of solid vibration beam gyroscope, the elements effecting the zero stability which effects the short term bias stability was discussed. The computed result shows that the main factors for short-term bias stability is transient solution error. The output signal has been filtered by the low pass filter, according to the characteristic of transient solution error. Simulation results demonstrate that low-pass filter can effectively suppress the error of output signal. In addition, the signal of solid state vibrating gyroscope filtered by low-pass filter agrees well with the simulation result. From the simulation and experiment data, the validity of the model and the feasibility of the filtering programs has been proved.

scholarly journals Computing efficiency of the three-stage interpolated low pass filters

2018 ◽  
Vol 28 (4) ◽  
pp. 21-27
Author(s):  
I. S. Savinykh ◽  
D. A. Chemasov
Keyword(s):  
Impulse Response ◽  
Computational Efficiency ◽  
Finite Impulse Response ◽  
Sampling Rate ◽  
Efficiency Coefficient ◽  
Transition Band ◽  
Pass Filter ◽  
Low Pass Filter ◽  
Low Pass ◽  
Low Pass Filters

Undoubted advantages of finite impulse response filters are their unconditional stability, the absence of limit cycles and the possibility of implementing a filter that does not introduce phase distortion. The disadvantage of such filters is the large cost required to compute the response. This paper considers three-stage interpolated finite impulse response low-pass filters. The maximum values of the interpolation factors are determined. Dependences of the coefficient of computational efficiency and the coefficient of increase in the registers of the three-stage interpolated low-pass filter on the values of the interpolation factors, the widths of the passband and the transition band are obtained. Relations for determining the optimal values of interpolation factors corresponding to the maximal value of computational efficiency coefficient are obtained. In addition, the dependencies of the maximum coefficient of computational efficiency and the optimal coefficient of increase in the registers of the three-stage interpolated low-pass filter on the widths of the passband and the transition band at the optimum values of the interpolation factors are obtained. Considered three-stage interpolated low-pass filters should be used in the case when the required stopband is significantly less than the sampling rate. In this case, three- stage interpolated filters require less computational resources for calculating the response than the two-stage interpolated filters or filter implemented by the transversal structure.

Design of Programmable Wideband Low Pass Filter with Continuous-Time/Discrete-Time Hybrid Architecture

2017 ◽  
Vol E100.C (10) ◽  
pp. 858-865 ◽  
Author(s):  
Yohei MORISHITA ◽  
Koichi MIZUNO ◽  
Junji SATO ◽  
Koji TAKINAMI ◽  
Kazuaki TAKAHASHI
Keyword(s):  
Discrete Time ◽  
Continuous Time ◽  
Hybrid Architecture ◽  
Pass Filter ◽  
Low Pass Filter ◽  
Low Pass
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