impulse response is a very important analysis of a control system, for example there is an AVR control system that controls the output voltage of a generator, when someone wants to design this controller, has to consider the worst condition(the very very bad disturbance which it is perhaps some time event for the system under control or maybe never happen) because the control system must be secure the generator from this possible event, in this example the worst condition can be Lightning, for very small period of time (Micro second), a very big voltage added to terminal voltage of generator,(Mega Volts), so control system of AVR must overcome this condition,

excuse me if my English is not well,

It is not really difficult to get the concept. When we say that we want to get the response of a system to an input, it basically means that we want to see how the system respond to every individual frequency element of the input signal (an arbitrary non-sinusoidal signal is a combination of more than one single-frequency elements). Now knowing this fact, in control systems we analyse the systems with two important signals as the input such as Step and Impulse signals. the first is useful for evaluating the system for transient responses (settling time, overshoot, etc) however the second one that is impulse response is meant to evaluate the response of the system for all frequency elements with the same magnitude. The only signal which contains all single-frequency elements with unit magnitude is Impulse (if you take the Laplace transform of impulse, it is 1 which means all frequencies have same contribution). So by having the impulse response of a system, we actually have the overall behavior of that system, which is very important.

I hope you got your answer.

In the context as outlined above it should be mentioned that the Laplace transformation of the impulse respose h(t) of a system gives the transfer function H(s).

Or vice versa: The inverse Laplace transformation of H(s) is identical to the impulse response h(t).

Hence, h(t) and H(s) are connected to each other via the Laplace transform.

Hi.

In signal processing, the impulse response, or impulse response function (IRF), of a dynamic system is its output when presented with a brief input signal, called an impulse. More generally, an impulse response refers to the reaction of any dynamic system in response to some external change. In both cases, the impulse response describes the reaction of the system as a function of time (or possibly as a function of some other independent variable that parameterizes the dynamic behavior of the system).

In all these cases, the dynamic system and its impulse response may be actual physical objects, or may be mathematical systems of equations describing such objects.

Since the impulse function contains all frequencies, the impulse response defines the response of a linear time-invariant system for all frequencies.

Mathematically, how the impulse is described depends on whether the system is modeled in discrete or continuous time. The impulse can be modeled as a Dirac delta function for continuous-time systems, or as the Kronecker delta for discrete-time systems. The Dirac delta represents the limiting case of a pulse made very short in time while maintaining its area or integral (thus giving an infinitely high peak). While this is impossible in any real system, it is a useful idealisation. In Fourier analysis theory, such an impulse comprises equal portions of all possible excitation frequencies, which makes it a convenient test probe.

for more interesting information visit for example

http://dsp.stackexchange.com/questions/536/what-is-meant-by-a-systems-impulse-response-and-frequency-response

or this address

http://lpsa.swarthmore.edu/Transient/TransInputs/TransImpulse.html

or here

https://ccrma.stanford.edu/~jos/fp3/Impulse_Response_Representation.html

be Sucessful

well my explanation may not be that practical but still i try to make it possible for you to understand. If you see a unit impulse signal it is only defined at t=0 secs having infinite magnitude, zero width and unit area, but in frequency you are giving all the frequencies at the systems's input to check its impulse response. In control theory we normally check stability of natural response using impulse signal.

"An impulse response of a person can be found by slap him on the face forcefully and then watching his reaction, if you dare! :)""

AoA!

if any one knows plz tell me

Mohammad Mahdi Momenzadeh ! i want to ask you that you have written " The only signal which contains all single-frequency elements with unit magnitude is Impulse" 

i don;t understand that how the impluse has single-frequency elements? plz illustrate the word single-frequency elements??? is that you mean that there is a signal which is has single frequency and in that single frequency there are many frequency elements??? if yes then what are these elements any example???? 

@ Imran Ali:

Fourier Theorem says every signal of this universe can be represented into multiple sinusoidal signals. Let say you represent a signal with three different siusoids then it means it has three fundamental frequencies or three single-frequency sinusoid.

PS: Study about Fourier Series and Transform to clarify more.

@ Daniyal Qureshi

Iam sorry to say Daniyal Qureshi ! you have not got my Question!! or i couldn't make yourself understand!! 

yeah! what you said that is gud and this is basics, and i think every one knows this  but my question was " how the impulse has all frequency elements of any system?? 

1.      Frequency domain

          a.      Fourier transform of a delta function (impulse) is constant, which means that it is not a function of any specific frequency. 

          b.      In other words, assuming that the impulse signal is created by superimposing of any combinations of sinusoidal signals, in frequency domain, delta is not a function of any frequency.

2.      Time domain

          a.      Impulse signal is

lim {sinc(2πft)}

as t approches       0

Which gives another perspective to analyze impulse signal. Based on the definition, the limit of sinc(x) is independent of the frequency.

3.      Any signal in time domain, f(t), can be made of an infinite sequence of delta functions of width Δt

as   Δt        approches to           0.

Response of a system is the sum of the delayed impulse responses, which is the convolution in time domain. In short, if we know the impulse response, since it is a linear system, we can find any sinusoidal output response. 

@Imran Ali

It\s not that complicated. As you know when we take a FT of a signal, we are actually evaluating the contribution of those fundamental elements(single-frequency sine or cosine) which are building that signal up! That means that we can superimpose  all these contributing elements to reconstruct the signal and they may lead the total response to attenuate or amplify in order to have the signal reconstructed. So by knowing that , we can come to the conclusion that in the impulse case, the contributing fundamental elements (which in this case are all frequencies and with the same share) are attenuating each other in all points but one and amplifying in that one common point that justify the infinite amplitude in one single time and zero in others.

sorry for late reply and I hope it helps.

@ Mohammad Mahdi Momenzadeh

thanks dear for response

dear its really helpful but one thing i don't understand  that you have written at last "but one and amplifying in that one common point that justify the infinite amplitude in one single time and zero in others."  

means at one point(that is impulse), amplifying that impluse making it magnitude infinte in single time(t=0) and t=0 for others???

yes then if i do this then HOW IT JUSTIFY THE RESPONSE OF SYSTEM??? means making one fundamental element's mag infinite which doesnot make sense to me

plz elloborate it more!!! that would be appreciable ...

I think, there is no PRACTICAL application for the impulse response (because such an impulse cannot be realized). But it has a rather important meaning in system theory because we can show that the LAPLACE transformation of the impulse response h(t) is identical to the systems transfer function H(s). This leads to another interesting relation: h(t)=d[g(t)]/dt  with g(t)=step response.

@Imran Ali

ok! let me tell you in this way! imagine an electrical circuit with infinite voltage sources each of which has a different frequency than other sources (infinite different frequencies each assigned to one source). I'm sure you know how to solve that circuit theoretically! (of course this case is just to clarify and  not for real!) imagine a black box which is fed by an ideal impulse signal (which you can never find in the reality). So this case is like feeding that black box with infinite number of sources like what I explained above. So in impulse case after finding the impact of each imaginary source with its corresponding frequency and superimposing all those impacts, you're going to see that the superimposing ends up in the response of that black box to the impulse and if that black box has no element (just wires connecting the input to the output) so the impacts of those input sources is going to be the superposition of all signals by those input sources instantaneously which results in the impulse itself!

I did my best to simplify the concept as much as I can. I hope you got your answer.

Impulse response is nothing but the natural response of a system. Its the output which is expected from a system when there will be a sudden spike input to a system. practically impulse signal can't be realized but a sudden and huge change in the input and the corresponding output is the impulse response.

In frequency domain it is nothing but an all pass filter as phase = 0 and magnitude =1. 

On the stability point of view if the impulse response is finite value for all bounded input to the system the system is stable.

In signal processing, the impulse response, or impulse response function (IRF), of a dynamic system is its output when presented with a brief input signal, called an impulse. More generally, an impulse response is the reaction of any dynamic system in response to some external change.

Infinite impulse response (IIR) is a property applying to many linear time-invariant systems. Common examples of linear time-invariant systems are most electronic and digital filters. Systems with this property are known as IIR systems or IIR filters, and are distinguished by having an impulse response which does not become exactly zero past a certain point, but continues indefinitely. This is in contrast to a finite impulse response (FIR) in which the impulse response h(t) does become exactly zero at times t > T for some finite T, thus being of finite duration.

 Finite impulse response (FIR) filter is a filter whose impulse response (or response to any finite length input) is of finite duration, because it settles to zero in finite time. This is in contrast to infinite impulse response (IIR) filters

The impulse response (that is, the output in response to a Kronecker delta input) of an Nth-order discrete-time FIR filter lasts exactly N + 1 samples (from first nonzero element through last nonzero element) before it then settles to zero.