Why h(n) is called impulse response in Convolution.

[venkat_walking]

I understand in my way that convolution is called multiplication of two signals, (one is called input signal and other is called impulse response).

I cant understand why impulse response, why not 2nd input signal.

I know that, I am having half knowledge about signal processing.

Please explain

Thanks

Venkat

 

[snikfreak]

Thats a great question,
I never though to ask lecturers during the classes,
but what i know is, convolution needs an impulse to have an output,
i'm just using this idea in Matlab, but mathematically i dont have enough knowledge about it,
lets wait for seniors to explain it,

---------- Post added at 17:52 ---------- Previous post was at 17:46 ----------

Moreover, impulse is needed to make frequency shifting, in other words if you insert another input signal which is not (impulse) you will get some different
shifting frequencies which will effect the original signal !!

 

[ernpao]

Hi, I'm not really sure since I don't know a lot about signal processing, but I think you are right that the 2nd signal can be referred as the "2nd input signal" since any 2 signals can be convolved.

The impulse response is a signal as well - it is the output signal of a system when it is fed a brief input signal (an impulse).

Now if a signal (let's say f) is convolved with the impulse response of a system (let's say system X), i think the result of the convolution is the output of system X when f is the input.

I guess the reason they call the 2nd signal the impulse response in your convolution is because the 2nd signal is an impulse response and because you are studying about systems. Using convolution to determine the output of a system is an application of convolution in signal processing.

 

[Shaheers]

ernpao is saying right, the reason why i say impulse response is that, it is a response of the system h at a particular time, its not even a signal, its a behavior of the system at particular time. . . is it clear. . . ?

after that I have a question that

in exam, if they tell to make a system for some specific application, can we use ideal filter impulse response that is mentioned in 2.4.1.1 Example 1 of the following link?
**broken link removed**

 

[iVenky]

Impulse response is a very simple concept.

Now let's talk about the system. We want to know about the system. For that I am going to send an impulse to the system and I see the output. An impulse is like the number '1' in normal mathematics.
If I want to know about an unknown 'x' and you can't find the value of 'x' unless you do some operation with it.(i.e. you can't access the unknown directly but only from the output of the operation). Then what I should do is to multiply that by 1 and find it's value (which you can see from the output). Once you know what that 'x' is, then you can easily find the output for other values by simply multiplying the input with 'x'. This is just an example to make you understand the concept.

So this what you do- You first find the output of the system for an impulse which is known as impulse response. Now take any signal. Split that signal into many impulses each with different amplitude corresponding to each point in the signal. Then the output of the system is simply the the output when you apply each individual impulses to the system which can be easily found out because you know the impulse response of the system. The combination of all gives the output for the entire signal. It may be confusing mathematically but I recommend you see this book that I have mentioned below to completely understand what I am telling.
The best book for DSP is "The Scientist and Engineer's guide to DSP" by Steven W Smith where there's no formula at all but only the concepts which are clearly described.

 

[klystron]

The impulse response of a circuit (filter) characterize the circuit in the time domain. The frequency domain equivalent is the frequency response ;the input impulse(Dirac) transforming to all frequency components*white noise) in the frequency domain

 

[ashiir]

iVenky is right.
Let's imagine that there is an unknown system characterized by h.
When you feed it with the input signal x, the output y would be convolution of x*h.
So, how can you find the output of this system? Firstly, you have to find what h is. But how to know?
The simply method to find is to feed this system with an impulse signal and see what the output is.
The impulse signal, like iVenky's post, is like '1' in Maths (its Laplace transform is 1). So you can characterized h by this.
Then, you can find its output from any input by multiplying this response with the desired input.

That's why h is called "impulse response".
Because h is characterized by impulse signal input.

 

[sani123]

Asalamualikum to all...

first thing there is the difference between the multiplication and the convolution....
in convolution there is the dot to dot multiplication (not simple multiplication) ....
and the other thing why we convolve the signal with impulse response for this firstly you have to understand that what is impulse response ...basically impulse response tells the behavior of that signal

 

[iVenky]

Asalamualikum to all...

first thing there is the difference between the multiplication and the convolution....
in convolution there is the dot to dot multiplication (not simple multiplication) ....
and the other thing why we convolve the signal with impulse response for this firstly you have to understand that what is impulse response ...basically impulse response tells the behavior of that signal

Yes convolution and multiplication are different. Impulse is just similar to '1' in mathematics. I have clearly mentioned in my post that it's just an example to make you understand.