What is Impulse response ?

Could anyone explain about impulse response of a linear system?
Is that can be stated as transfer function, h(t) ?

The impulse response is a mathematical concept that can be approximated in the real world. It is the output of a circuit when an ideal impulse (zero width pulse with unit area) is applied to the input. The Laplace transform deals with this.

The spectrum of an ideal impulse is flat and so the frequency shape of the resulting output of the network is the frequency response of the network.

Let's say that you have a SYSTEM .this can be mechanical electronic or other
and you aplply an input and want to see how this system behaves .The problem is that for a different signal you will get a different output ..So is hard to predict what the RESPONSE of the system will be for a particuliar shape of input signal
So one way to calculate this will be to input an INPULSE of 0 widh and infinitly big but the area remains constant ( this is called the Delta function)
Is a mathematical trick .Now any function or input signal can be a written as a collection of those pulses .. so by calculating THE INPULSE RESPONSE of one pulse .the collection of them is easier .this leads to the TRANSFER FUNCTION .This is done with the LAPLACE transform .
so basically is a very simple CONCEPT, but the formulation is of high level !

Impulse response of a linear system is nothing but the response of a system when input is impuse.ie when we apply impulse as input to a system ,the o/p of the system is called impulse response.since the laplace transform of impulse function is unity hence the inverse laplace laplace transform of system transfer function is nothig but impulse response.

take a look at this small "tutorial"
https://zone.ni.com/devzone/conceptd.nsf/webmain/A9079524FB29D67986256D7B0079E2FD
or jump directly to some book like:

- Signals and Systems by Alan V. Oppenheim
- Control Systems by Kuo

You should go to the library and read chapter 1 to 2
of those books titled " Signals and Systems".
Famous authors at this field are Oppenheim,Lathi,Haykin......etc.
You can find many informational figures about impluse and its response,convolution in those books!


Good luck!

Added after 25 minutes:

You should go to the library and read chapter 1 to 2
of those books titled " Signals and Systems".
Famous authors at this field are Oppenheim,Lathi,Haykin......etc.
You can find many informational figures about impluse and its response,convolution in those books!


Good luck!

Could anyone explain about impulse response of a linear system?
Is that can be stated as transfer function, h(t) ?

Impulse response of a system actually tells us how the system would behave when various frequencies (i.e. signals) are appliend to the system. Impulse itself is not a transform but an ideal signal and is used in transforms of a system to frequency domain.

In the language of mathematics, the impulse response of a linear transformation is the image of Dirac's delta function under the transformation.
i.e

δ =1, if n=1; and
δ =o if n≠1;

In control theory the impulse response is the response of a system to a Dirac delta input. This proves useful in the analysis of dynamic systems: the Laplace transform of the delta function is 1, so the impulse response is equivalent to the inverse Laplace transform of the system's transfer function.

The Laplace transform of the impulse response function is known as the transfer function. It is usually easier to analyze systems using transfer functions as opposed to impulse response functions. The Laplace transform of a system's output may be determined by the multiplication of the transfer function with the input function in the complex plane, also known as the frequency domain. An inverse Laplace transform of this result will yield the output function in the time domain.

To determine an output function directly in the time domain requires the convolution of the input function with the impulse response function. This requires the use of integrals, and is usually more difficult than simply multiplying two functions in the frequency domain.

Impulse response of a linear system is nothing but the response of a system when input is impuse.ie when we apply impulse as input to a system ,the o/p of the system is called impulse response.

Frequency spectrum of Dirac function, unity pulse with duration equal zero and infinite amplitude, is continious spectrum with amplitude equal to one and for frequencies from -∞ to +∞. Responce of transfer function in frequency domain will have the same shape as amplitude/frequency charactheristics of the transfer function.

it is like a tranfer function. it describes the input and output characteristics of a system.
it is called impulse responce because when an impulse is given the output obtained can be easily helpful in determining the responce of system by convolving it with an unknown signal.
if u want t know further go through "sisgnals and system" by oppenhiem chapter no 1

wcz said:

Could anyone explain about impulse response of a linear system?
Is that can be stated as transfer function, h(t) ?

Click to expand...

Hi wcz,

look at the picture, we have a system that we don't know its transfer function H(w) = TF{h(t)}

a technic to find H(w) is to excite the system by an impulse and then mesure the output of the system Y(w). we use an impulse because of its Fourier Transform is 1.

we have Y(w) = H(w).X(w), X(w)=1 (impulse) then H(w)=Y(w).

i.e: the output of any system excited by an impulse is its transfer function.

aze.

yes, h(t) is a linear's impulse response.

best regards

wcz said:

Could anyone explain about impulse response of a linear system?
Is that can be stated as transfer function, h(t) ?

Click to expand...

note that \[h(t)\] is called impulse response and \[H(\omega)\] is called transfer function.

coming to the impulse response, it is just the response of the system when a unit impulse \]\delta(t)\[ is applied to the system.

thnx

purna!\]

Added after 1 minutes:

note that \[h(t)\] is called impulse response and \[H(\omega)\] is called transfer function.

coming to the impulse response, it is just the response of the system when a unit impulse \]\delta(t)\[ is applied to the system.

thnx

purna!

when u want to check a system how it works for different frequencies, u have to either generate all those frequencies and see the response or else simply check with an impulse signal. impulse is the elementary component of all signals. and it contains all frequencies from -inf to +inf.

eltonjohn said:

Let's say that you have a SYSTEM .this can be mechanical electronic or other
and you aplply an input and want to see how this system behaves .The problem is that for a different signal you will get a different output ..So is hard to predict what the RESPONSE of the system will be for a particuliar shape of input signal
So one way to calculate this will be to input an INPULSE of 0 widh and infinitly big but the area remains constant ( this is called the Delta function)

Click to expand...

This approach sounds like a frequency sweep using a sweep oscillator in order to find out the frequency response of a circuit, except it is done using an inpulse of 0 width and infinitely big amplitude???

I don't understand how you can have a signal/pulse? that has 0 width and amplitude infinitely big. Sorry I am new to this and I am struggling to learn about this also...

I don't understand how you can have a signal/pulse? that has 0 width and amplitude infinitely big

Click to expand...

practically its not possible. it is only an theoretical/mathematical approach.

I don't understand how you can have a signal/pulse? that has 0 width and amplitude infinitely big

Click to expand...

practically speaking is imposible but some people has done this way:
it is applied a very fast pulse. The derivative of an ideal pulse is an impulse.
There is a lot of this in NIST library. You can find some info in **broken link removed**

Just wanted to point out that.. impulse response h(t) is for only LTI (linear and time invariant) systems.

hi there is no rule that there is impulse response only for LTI systems. It just says that it is the response of the system for an impulse input. There is no restriction on the system to be LTI.

thnx

purna!