Solving for the impulse response of a discrete time system?

In summary, the coefficient of y_n[k] is A_0, which is represented by b_0/a_0, but where b_0 comes from is unknown.
  • #1
Jayalk97
45
5
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.
 

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  • #2
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
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
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
FactChecker said:
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
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

FactChecker said:
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
Sorry, my post #4 should have been saying b0, not a0. I will edit it.
 
  • #8
FactChecker said:
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.
 

1. How do you determine the impulse response of a discrete time system?

To determine the impulse response of a discrete time system, you can use the impulse response function, which is a mathematical representation of the system's output when the input is an impulse signal. This function can be calculated using various methods such as convolution, Fourier transform, or Z-transform.

2. What is the significance of finding the impulse response of a discrete time system?

The impulse response of a discrete time system provides valuable information about the system's behavior and characteristics. It can help in understanding how the system responds to different inputs, as well as in designing filters and predicting the system's output for different inputs.

3. How does the impulse response differ from the step response of a discrete time system?

The impulse response and step response of a discrete time system are both used to analyze the system's behavior. However, the impulse response represents the system's output for an input of an impulse signal, while the step response represents the system's output for an input of a step signal.

4. Can the impulse response of a discrete time system be measured experimentally?

Yes, the impulse response of a discrete time system can be measured experimentally by sending an impulse signal as an input to the system and recording its output. However, this method may not be feasible for complex systems, and mathematical methods are often used instead.

5. What are some real-world applications of solving for the impulse response of a discrete time system?

Solving for the impulse response of a discrete time system has various real-world applications, such as in audio and signal processing, control systems, image processing, and communication systems. It is also used in fields like acoustics, seismology, and astronomy for analyzing and modeling systems and signals.

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