Solving for the impulse response of a discrete time system?

  • #1
45
5

Main Question or Discussion Point

Hey guys I was just studying for finals and I came across something in my textbook that either wasn't explained properly or something I just don't get.
upload_2017-12-9_22-48-42.png

So this page explains that the coefficient of y_n[k] is A_0, which is represented by b_0/a_0, I can see that a_0 is determined by multiplying the characteristic modes of the equation, but I'm not sure where b_0 comes from. Thanks for any clarification.
 

Attachments

Answers and Replies

  • #2
45
5
Bump. I just need a little clarification on how to find a_0 and b_0, I have a pretty good grasp on the concepts.
 
  • #3
Stephen Tashi
Science Advisor
6,952
1,201
If want help from the general mathematical population, you should give a complete statement of the problem. A communications engineer might be able to infer what is in Appendix 9.1, what is in example 3.4, and how ##a_0## and ##b_0## are defined. However, the typical helpful mathematician won't know what you are asking.
 
  • #4
FactChecker
Science Advisor
Gold Member
5,304
1,899
b0 is the coefficient in the b0f[k] term on the right hand side of 9.36. You can trace where it comes from and goes to from there. In this case, there is no such term, so b0 = 0.

EDIT: This post originally had a0s where it should have been b0s. It has been corrected.
 
Last edited:
  • #5
45
5
a0 is the coefficient in the a0f[k] term on the right hand side of 9.36. You can trace where it comes from and goes to from there. In this case, there is no such term, so a0 = 0.
Ohhhhh thank you so much! I would have picked up on it if they used an example that had a nonzero b_0 haha.
 
  • #6
donpacino
Gold Member
1,439
282
Typically a_0 and b_0 would be t=0 coefficient of a typical IIR filter. See the below example

http://123.physics.ucdavis.edu/week_5_files/filters/digital_filter.pdf

a0 is the coefficient in the a0f[k] term on the right hand side of 9.36. You can trace where it comes from and goes to from there. In this case, there is no such term, so a0 = 0.
I disagree... look at 9.35 (or 9.36) and reference page 10 of my above link.
a_0=-0.16
b_0=0
 
  • #7
FactChecker
Science Advisor
Gold Member
5,304
1,899
Sorry, my post #4 should have been saying b0, not a0. I will edit it.
 
  • #8
45
5
Sorry, my post #4 should have been saying b0, not a0. I will edit it.
I picked up on that, I probably should have mentioned it but I was just excited it clicked and just went back to studying haha. Thanks regardless.
 

Related Threads for: Solving for the impulse response of a discrete time system?

Replies
2
Views
10K
  • Last Post
Replies
4
Views
3K
Replies
9
Views
906
  • Last Post
Replies
3
Views
1K
  • Last Post
Replies
1
Views
2K
  • Last Post
Replies
6
Views
5K
  • Last Post
Replies
4
Views
7K
  • Last Post
Replies
1
Views
4K
Top