Impulse response? I need a bit of help with this if anyone can?

In summary, the speaker is a student who studied music and English in their undergrad but is struggling with impulse response in their postgrad studies. They are asking for help with some exercises from their lecture notes and are confused about how their lecturer got the answers. The conversation includes examples and solutions for different exercises, including finding the output of a continuous system, using convolution to determine the output of an electrical system, evaluating an integral, and finding the frequency-response function of a system. The speaker is not familiar with these concepts and is asking for step-by-step explanations.
  • #1
lizm
8
0
hey, i did my undergrad in music and english and now am lost beyond reckoning with the impulse response stuff in my postgrad. Could anyone help with these exercises? They're examples from my lecture notes and have no idea how my lecturer got the answers. Please help?

Ex.1) Show that x(t)*h(t) = h(t)*x(t)
EH? ANY IDEAS?

Ex.2) The unit response of a continuous system is h(t)=3e -2t-5e -4t/sup].
If the input is modeled as x(t)= [delta](t)-2[delta](t-1)+[delta](t-2.5), find the value of the output at time=1.5s.
Ans: y(t)=0.717 at t=1.5s.

Ex.3) An electrical system has unit-impulse response h(t)= 3te -4t . If a unit step function u(t) is applied to the system, use the convolution integral to determine the value of the output after 0.25s.
Ans: 4.95 x 10 -2 V
What's the unit step function for a start?

Ex.4) Evaluate the integral [integral infinity to minus infinity] f 1 (t)f 2 (t)dt
Where f 1 = 2sin (2000[pie]t) and f 2 (t) = [delta] (t-0.25 x 10 -3 )
Ans: 2
How do they get a pure whole number out of all those symbols?
 
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  • #2
I'm doing a Music Technology course so didn't see all this maths coming at me... Thank you to anyone who can help. We have an electrical engineering lecturer and he is of the opinion that we know all of this and hasn't explained anything properly at all. I'm only a music student! So, I would really apperciate anyone who has a bit of time to go through the exercises step-by-step. Thanks
 
  • #3
And we just got this exercise to look over and see if we have any problems...
Frequency Response
Ex. A pulse, modeled as the weighted impulse 2 [ delta] (t) , is applied to a system and produces the response y(t) = 6e -2t - 4e -3t . What is the frequency-response function of the system.
Ans. H (j [omega] ) = 5+j [omega] over (2+ j [omega] )(3+ j [omega] )

Any help?
 

1. What is an impulse response?

An impulse response is a mathematical representation of the output of a system in response to an impulse input. It is commonly used in signal processing and engineering to analyze the behavior of a system.

2. How is an impulse response measured or calculated?

An impulse response is typically measured by sending a short, sudden burst of energy (known as an impulse) into the system and recording the resulting output. It can also be calculated using mathematical models and simulations.

3. What information can be obtained from an impulse response?

An impulse response can provide information about the characteristics of a system, such as its frequency response, time delay, and distortion. This information is useful in understanding the behavior and performance of the system.

4. How is an impulse response used in practical applications?

An impulse response is commonly used in audio engineering, room acoustics, and digital signal processing. It can be used to model and simulate the behavior of systems, design and test filters, and improve the overall sound quality in audio recordings.

5. Can an impulse response be modified or manipulated?

Yes, an impulse response can be modified or manipulated in various ways, such as filtering, equalization, and convolution. This allows for the creation of different effects and sound enhancements in audio applications.

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