I cant understand the impulse response in convolution

In summary, the conversation discusses finding h-1[k] in a given graph, with an impulse response of δ[n+1]. The solution is provided, but the process of deriving it is not explained. The expert summarizes that h[n] is not calculated but used in a later step and confirms that their assumptions align with the context of the conversation.
  • #1
Jncik
103
0

Homework Statement



i have this graph

[PLAIN]http://img858.imageshack.us/img858/1346/56954457.png [Broken]

and i need to find h-1[k]

i don't understand, i know that the impulse response is the response for input -> δ[n], in this case it will be δ[n+1], but i don't understand how to calulate the response..
my book doesn't say anything it just has the solution which is the following

[PLAIN]http://img96.imageshack.us/img96/7766/61813044.png [Broken]

can you show me how he figured this out?? you d save my life
 
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  • #2
You're leaving out some context, so I'm going to make a few educated guesses.

I suspect we're talking about some signal that is passed through a filter, which would yield an output signal.

In this case the input signal would be modeled with x[n].
The filter would be modeled with h[n].
And you would have an unmentioned output signal that we'll call y[k].

The correlation would then be given by the following equation:
10ff3eff0b11291928b4035623b1a2f9.png


Basically, what I'm trying to say, based on my series of assumptions, is that h[n] is not calculated here, but given, to be used in a later step.

Do any of my assumptions and my tentative conclusion come near the reality?
 
  • #3
yes they do, thank you very much, i just wasnt sure that he gave us this to find out the y[n]
 

1. What is the impulse response in convolution and why is it important?

The impulse response in convolution is a mathematical concept that describes how a system responds to an impulse input. It is important because it allows us to analyze and understand the behavior of a system, such as an electrical circuit or signal processing system.

2. How is the impulse response calculated in convolution?

The impulse response is calculated by convolving the input signal with a delta function, which has a value of 1 at 0 and 0 everywhere else. This process involves multiplying the input signal by the delta function at every time step and summing the results.

3. What does the impulse response tell us about a system?

The impulse response tells us how a system will respond to any input signal. It provides information about the system's frequency response, stability, and other important characteristics.

4. How does the impulse response relate to the frequency response?

The impulse response and frequency response are closely related. The frequency response is the Fourier transform of the impulse response, which means it provides information about how the system responds to different frequencies in the input signal.

5. How can the impulse response be used in practical applications?

The impulse response is used in various practical applications, such as signal processing, audio and video processing, and control systems. It helps in designing and analyzing systems, predicting their behavior, and improving their performance.

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