What is Impulse response ?

[ciitv]

Let make it simple by taking an analogy. What is slap response ? The way you respond when somebody slaps you. What is impulse response then ? The way a system responds at the output when an impulse(think of it as an electrical 'surge' for time being) is applied at the input.

Is it applicable to only LTI systems ? Just think about it. Can you apply an electric surge voltage to any device, say a TV. Yes. Is TV a linear device. Most part of it is no. Does the TV respond to the surge -> yes . So impulse response applies to all systems.

But why make a big fuss about LTI systems ? With non linear device and impulse response you can't predict response to any signal. But with LIT you can . So LTI and impulse response make a deadly pair

 

[v_c]

I think we are missing the meaning behind the impulse response here and whether or not we can create very narrow pulses to imitate the ideal impulse.

Whether or not something is an impulse does not really depend on the shape of the waveform but what its duration is with respect to the system it is being appllied. Let me explain.

Let's say you have a simple RC filter and you want to find it impulse response. To do this, you have to apply an impulse voltage at the input and measure its response (the impluse response) across the capacitor. But how narrow should you make the impulse width? Well, let's say the time constant of the RC circuit is 1 second (RC=1). Then, if you make the width of the pulse to be \[1\mu s\], then for all practical purposes, that pulse will feel like an impulse to the RC circuit.

Now the other thing to consider is the \[weight\] of the impulse, that is the are under the pulse itself. If you applied a voltage of 5V with \[1 \mu s\] duration, then the weight of the impulse is \[5 \mu V \cdot s\]. Note that the units of V-s, is actually flux, which may also be expressed in Webers (Wb).

Here's the most important idea. As long as you apply a pulse that is much, much less than the time constant of the circuit and the applied waveform has the same area, the response will be the same. What I am trying to say is that it is the area of the curve that is important, not necessarily the shape.

Try this with a circuit simulator. Apply a square pulse, triangular pulse, anything that you like. Just make sure the are is the same and the time duration is small. Look at the output of your RC circuit -- amazing!

Best regards,
v_c

 

[newmin]

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!

Right.

However, there is a rule that the impulse response is only for the LTI systems if you want to say the output signal is the convolution of the input and the impulse response. As I see it, most people are discussing about how impulse response (of LTI systems) can be useful because of tools like Laplace Transform and the handiness of frequency domain analysis.

 

[dosto]

hey comsians your explanataion about impulse is totally wrong, impulse input is equal to 1 only if t is 0. in other times it is 0.

 

[v_c]

hey comsians your explanataion about impulse is totally wrong, impulse input is equal to 1 only if t is 0. in other times it is 0.

That is the Kronecker delta function \[\delta[k]\] from discrete time systems, which is 1 at \[k=0\] and is 0 everywhere else for integer values of \[k\]. The Dirac delta function is uses for continuous systems and it is characterized better by its area than its amplitude. Its amplitude if concentrated at as single continous timepoint (say t=0) is infinity.

Best regards,
v_c

 

[JoseLeonardo]

You can read, Signals and Systems by Oppenhiem, Signals and Systems by Haykin, Digital Signal Processing by Proakis.

 

[k.gurunath]

Before posting to this thread let me say this....
There are so many signals say infinite signals in the nature which may range from small noise to cosmic signals generated in sky.
If there are so many signals in nature how can one design the system because the system has to respond to so many signals.
So we genaralise any signal as multiplied by 1 ,but 1 is nothing but a delta function
This function exists only when the parameter of delta function is 1
When a system is designed to such a function the output can be studied.
So when such a signal is fed to a system the output generated is h(t) which is a convolution of this signal with impulse.
Hence the name impulse response.

P.s: please note that the impulse is a basic signal which has no time ( ideally zero time ) and amplitude being 1,the area under this signal is also 1.

Added after 9 minutes:

sorry for the previous thread reply
There is a small correction read the line as
.......the parameter of the delta function is zero i.e., del(0)=1...........

 

[neils_arm_strong]

Impulse response is the response of a system for impulse input.Any signal can be approximated by a number of impulses and the o/p of the signal can be approxiamted if we know the impulse response.

 

[Prakash]

Impulse response of a linear system is the response of a system when input is impulse.
When we apply impulse as input to a system ,the o/p of the system is called impulse response.

Go through Signals and Systems by Alan V. Oppenheim for details

 

[dreamcard]

impulse response is the output of a (linear) system that fed by a dirac function input

 

[starfish]

The output produced by a Linear Time Invariant System due to an impulse at the input in called the impulse response. Impulse response completely charcterizes an LTI system and if u find the impulse response of a particular system then its output can be calculated for any input by convolving the impulse response and the input.

 

[hlasy]

Many people have posted thier views and mine will probably be a repitition of thiers. Let me put it non mathematically.

If I was asked to test my design. Testing it by feeding it with a particular frequency (say a sine wave ) is not sufficient. As we dont know how the system behaves at other frequencies.

Logically this would mean giving all the infinite possible input frequencies to our design before we are confident of its performance at the other frequencies.

On the other hand. If i were to feed an impulse input whose response covers the entire frequency spectrum, in one single input I get a fair amount of confidence on the performance of the design.

BR

hlasy