# What is Response function: Definition and 22 Discussions

Frequency response is the quantitative measure of the output spectrum of a system or device in response to a stimulus, and is used to characterize the dynamics of the system. It is a measure of magnitude and phase of the output as a function of frequency, in comparison to the input. In simplest terms, if a sine wave is injected into a system at a given frequency, a linear system will respond at that same frequency with a certain magnitude and a certain phase angle relative to the input. Also for a linear system, doubling the amplitude of the input will double the amplitude of the output. In addition, if the system is time-invariant (so LTI), then the frequency response also will not vary with time. Thus for LTI systems, the frequency response can be seen as applying the system's transfer function to a purely imaginary number argument representing the frequency of the sinusoidal excitation.Two applications of frequency response analysis are related but have different objectives.
For an audio system, the objective may be to reproduce the input signal with no distortion. That would require a uniform (flat) magnitude of response up to the bandwidth limitation of the system, with the signal delayed by precisely the same amount of time at all frequencies. That amount of time could be seconds, or weeks or months in the case of recorded media.
In contrast, for a feedback apparatus used to control a dynamic system, the objective is to give the closed-loop system improved response as compared to the uncompensated system. The feedback generally needs to respond to system dynamics within a very small number of cycles of oscillation (usually less than one full cycle), and with a definite phase angle relative to the commanded control input. For feedback of sufficient amplification, getting the phase angle wrong can lead to instability for an open-loop stable system, or failure to stabilize a system that is open-loop unstable.
Digital filters may be used for both audio systems and feedback control systems, but since the objectives are different, generally the phase characteristics of the filters will be significantly different for the two applications.

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1. ### Help Understanding Response Function $$H(\omega)$$

$$<H(\omega)>=\sum_{j} χ_{HAj}h_j(\omega)$$ Where $$χ_{HA}=\frac{1}{2\hbar} Tr{{\rho}[{H(t)},{A(0)}]}$$. But $$[H(t),A(0)]=[H_o,A(0)]-[A(t)h,A(0)]=-h_0 cos(\omega t)[A(t),A(0)]$$. So $$χ_{HA}=-\frac{1}{2\hbar}Tr(\rho h_0 cos(\omega t)[A(t),A(0)])=-h_0cos(\omega t)χ_{AA}$$. Then...
2. ### A What is the meaning of "modulated physical systems"?

In particular I'm studying the paper "Theory of dynamic response functions of periodically modulated physical systems" by Lovesey et al. and "modulated system" are mentioned many times. My thesis advisor recommend to me reed this paper but is very confuse, any reference you can give me in...
3. ### A Longitudinal and transverse response function

I was reading the book "finite temperature field theory" (https://www.amazon.com/dp/0521820820/?tag=pfamazon01-20) and encountered a problem on page 111 about linear response theory. Consider a system with some conserved baryon matter perturbed by a source J_\mu, coupled to the baryon current...
4. ### Acceleration amplitude of a damped harmonic oscillator

Homework Statement The acceleration amplitude of a damped harmonic oscillator is given by $$A_{acc}(\omega) = \frac{QF_o}{m} \frac{\omega}{\omega _o} \sqrt{\it{R}(\omega)}$$ Show that as ##\lim_{\omega\to\infty}, A_{acc}(\omega) = \frac{F_o}{m}## Homework Equations \it{R}(\omega) =...
5. ### Locate the poles of the response function for an LRC circuit

Homework Statement Locate the poles of the response function \alpha(\omega) in the complex plane for an LRC circuit. Homework Equations \alpha(\omega)=\frac{-i\omega}{L}\frac{1}{\omega_0^2-\omega^2-i\omega\gamma} \omega_0^2=\frac{1}{CL} \gamma=\frac{R}{L} The Attempt at a Solution So we've...
6. ### Transfer Function vs Frequency Response Function

Ive read other threads on here about this and am still slightly confused about it. I did a little experiment; and I am hoping someone can help shed some light on the results. The experiment: 1. Create a system: modeled after a simple spring-mass-damper with mass=1 damping zeta=.1, natural...
7. ### Can the system response function be calculated?

Suppose we represent the input information as a (nx1) column vector, the output information as another (nx1) column vector and the system response function as a (nxn) matrix. My question, is it possible to calculate the values of the cells of the matrix knowing the input and the output? For...
8. ### Frequency response function of periodic-stiffness model of system

Hi, I'm analyzing a 3 dof undamped system with discrete springs and masses. Three of the springs have time-dependent stiffness, following periodic law (with period T), they are modulated at the same frequency but with a phase difference of 120 deg one from the other. So this is my system: (M *...
9. ### On deriving response function in simple low pass filter

Homework Statement I have a problem where the circuit is as follows: (pic attached I hope) but if you can't see it it's just a power source (AC), resistor and inductor with 2 terminals across the inductor (from were you measure the voltage). I want to derive the response function, and I am...
10. ### Dipole excitation response function - physical interpretation

Hi everyone, I'm a new member but it's not the first time I look at the forum. Well, I don't know if this is the right section to post my question. I think it is related to quantum mechanics interpretation too. Anyway, let's have a look at my problem. I've computed cross section for photon...
11. ### Impulse Response Function Problem

I attempted by inputting u(τ-t)u(t-τ) into the second part of the integral. Since I want to change the second part of the integral to go from [+∞, -∞]. And as for first part of the integral I added a u(t-τ) term after the x(τ) to change the integral from [t,-∞] into [+∞, -∞]. I am not sure if I...
12. ### Frequency Response Function- fundamentals

I undestand the following concerning the frequency response function; Frequency response function is a fundamental measurement that isolates the dynamic properties of a mechanical structure. It describes the input output relation between two points of a structure as a function of...
13. ### How to find the transfer function (frequency response function) given the EOM

for a given spring/damper system the equation of motion is: [PLAIN]http://img600.imageshack.us/img600/2140/equation1.png where x is the displacement of a mass from a fixed point d is a damping constant L1 and L2 constant lengths k1 and k2 are 2 spring constants...
14. ### Frequency response function (polar diagram)

This isn't really a homework question but I felt this is the most relevant section for this. I therefore apologize for not following the standard post template. I was going through my electrical engineering notes on frequency response functions. It was explaining how to plot frequency response...
15. ### How Do You Convert Frequency Response Function H(iw) to Time Domain h(t)?

I am trying to find the frequency response function given the input and output spectra from the picture i got that X(iw) = iU(w)U(2-w) - iU(w+2)U(w) and that Y(iw) = iwU(w)U(1-w) - iwU(w+1)U(w) So H(iw) = Y(iw)/X(iw) and H(iw) = wU(1-w) - wU(w+1) / U(2-w) - U(w+2) i am having...
16. ### EM response function of the Phase Action of a BCS superconductor

EM response function of the "Phase Action" of a BCS superconductor Hello, I am looking for a paper in which people calculated the EM response of phase action of A BCS SC. In the book "Condensed Matter Field Theory" by Altland and Simons, on page 393 they mention such a thing in the discussion...
17. ### Impulse response function & Laplace transforms

i am given the Laplace transform of an impulse response function, as well as its input. i am supposed to find its output. H(s) = 1/s2 + s + 1 x(t) = sin2(t-1)U(t-1) what i have done so far is the following: i know that Y(s) = H(s)X(s) and from this i can easily find y(t) so i found X(s)...
18. ### Identifying Impulse Response Function from State Equations

Hi, given the state equations of a system, x(dot) = Ax + Bu y = Cx is the impulse response function of this system C(e^(At))B? If not, how can i identify the impulse response from a given state equations? Please advise. Thank you.
19. ### Frequency Response Function - Random Vibration

Hi looking for some help on the below I'm a little bit stuck. The effect of an earthquake on an elevated water tank is to be investigated. The water tank has mass m=2x10^6 kg and natural frequency wn=10.6 rad/s and a damping coefficient of 12% critical damping. Ground acceleration can be...