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Dynamic Systems and Control Theory
Published in Mohammad Monir Uddin, Computational Methods for Approximation of Large-Scale Dynamical Systems, 2019
Another common and frequently used tool to analyze the system is the step response. Typically, this is the first characteristic step response to be analyzed for a newly designed system. Similar to the impulse response, the step response of a system is the output of the system when a unit step function is used as the input.step function(Unit step function)The unit step function is defined asunit step functionustep(t)={0,ift<01,ift≥0
Spectral Analysis
Published in Colin H. Hansen, Foundations of Vibroacoustics, 2018
The frequency response function, H(fn), is defined as: () H(fn)=Y(fn)X(fn)n=0,1,…,(N−1)The frequency response function (FRF), H(fn), is the Fourier transform of the system impulse response function, h(tk). The FRF is a convenient way of quantifying the relative amplitude of and the phase between two signals as a function of frequency. The impulse response of a system is the system output as a function of time following an impulse input (very short, sudden input)
DSP Technology
Published in Douglas Self, Audio Engineering Explained, 2012
When the linearity property is combined with the time-invariance property to form a linear time-invariant (LTI) system, then the analysis of systems is very straightforward. Because a sequence can be represented as a sum of weighted delayed impulses as shown in Eq. 15.2, and an LTI system response is the sum of the component responses of the sequence components as shown in Eq. 15.7, the response of an LTI system is completely determined from its response to an impulse. Since an input signal can be represented as a collection of delayed and scaled impulses, the response to the full sequence is known. The response of a system to an impulse is commonly referred to as the impulse response of the system. Mathematically,
Use of moving average filter for regularization of the transfer function based on Green's function method (TFBGF) to solve an IHCP
Published in Inverse Problems in Science and Engineering, 2020
Ana Paula Fernandes, Marcelo Braga dos Santos, Gilmar Guimarães
From the properties of the impulse function, we have Therefore, the impulse response of the problem is obtained as considering that , and G is given by Equation (16). Thus, the analytic expression for the impulse response of the problem is given by The transfer function is given by the Laplace transform of the impulse response, so . The heat flux is estimated by , where is experimentally acquired and the impulse response is defined analytically by Equation (20).
Room Response Equalization of Non-Minimum Phase Systems Using Kautz Filter and Sparse Autoencoder: A Hybrid Approach
Published in IETE Journal of Research, 2022
Sayanti Chaudhuri, Debangshu Dey, Sugata Munshi
Room acoustics deals with the creation, propagation, and perception of sound inside closed spaces. These spaces may be auditoria, lecture rooms, concert halls, etc. Important signatures of the acoustical property of a room, and in fact of any enclosure in general, are the room impulse responses (RIR) [1]. The RIRs provide a vivid representation of the acoustic behaviour between the two points: the source and the receiver within the room. Thus, different receiver and source positions will lead to different RIRs for the same room. It is predominant that while reproducing sound in a closed room, reflections and reverberations often arise by mutilating the sound produced by an acoustic source, thus affecting listening and attention. In this regard, the concept of room response equalization (RRE) has come into being. RRE deals with improving the sound quality produced in real environments such as cinema theatres, home theatres, car hi-fi systems [1,2]. RRE is also essential in implementing hearing aid applications [3]. It is often seen that the hearing aid users suffer several problems such as unwanted noise and acoustic reverberation which eventually decrease intelligibility and acoustic comfort. There are many papers [4–6] that portray the noise reduction and speech dereverberation algorithms in context to the hearing-aid implementation. But, apart from the intelligibility and comfort issues, room response equalization is essential for sustaining the original acoustic scenario to the hearing-aid users. Efforts have been made by researchers over decades to enhance the listening experience under reverberant conditions. A plethora of design techniques have been proposed for RRE.
Detection of spatially sparse damage using impulse response sensitivity and LASSO regularization
Published in Inverse Problems in Science and Engineering, 2019
Chandler B. Smith, Eric M. Hernandez
Results from [11] indicate that the increase in modal information improves the effectiveness of the optimization, and that additional modal information allows each perturbed element a more unique effect on the global response; an important characteristic for successful inversion in convex optimization theory. In this paper, the framework in [11] is reformulated such that modal information and uniqueness are improved, while at the least preserving the level of modal spectrum incompleteness conducted in [11]. The impulse response is the natural choice for satisfying the above criteria because it contains information on mode shapes, natural frequencies, and damping.