Solving for the impulse response of a discrete time system?

[Jayalk97]

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.

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.

 

[Jayalk97]

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.

 

[Stephen Tashi]

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.

 

[FactChecker]

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.

 

[Jayalk97]

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.

 

[donpacino]

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

 

[FactChecker]

Sorry, my post #4 should have been saying b₀, not a₀. I will edit it.

 

[Jayalk97]

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.