How Do I Approach Solving Z-Transform System Problems?

[Stan85]

Hi,

I have this question about the system diagram I have attached. I don't know how I should really start it. I don't expect any solutions from you. I just need to get access to similar questions and some resources that help me understand what I should do.
Any help will be much appreciated.

In the diagram attached, R(z) is the z-transform of the system's input r[n], C(z) is the z-transform of the system's output c[n], and G(z) and H(z) are the transfer functions of the subsystems given by:

G(z) = z / (z+1)
H(z) = 6 / (z-7)

(a) Determine the unit-pulse response of the overall system.

(b) Compute the step response of the overall system.

Thank you

 

[Valkarie]

for your help.To answer questions about a system diagram, it can be helpful to start by familiarizing yourself with the fundamentals of system diagrams and their components. This could include understanding the different types of system diagrams, such as block diagrams and signal-flow diagrams, as well as the different components that can be used, such as transfer functions, impulse responses, and step responses. Additionally, you can use resources such as textbooks and websites to learn more about the techniques used when analyzing the performance of systems. Once you have a better understanding of the basics of system diagrams, you can then move on to researching and learning about the specific techniques used to analyze particular questions, such as determining the unit-pulse response and computing the step response. You can find resources online that provide step-by-step solutions to these types of questions, so you can use them to get an idea of what the process looks like. Additionally, tutorials and videos can be helpful in giving you a better visual understanding of how to approach these problems. Good luck with your question!

 

[Mene]

for reaching out and seeking assistance with your question. I can provide you with some resources and guidance to help you understand and approach this problem.

First, it's important to understand the concept of the z-transform and how it relates to discrete-time systems. The z-transform is a mathematical tool used to convert a discrete-time signal into its frequency domain representation. It is similar to the Fourier transform, but it is specifically designed for discrete-time signals.

To solve this problem, you will need to use the properties of the z-transform, such as linearity, time shifting, and convolution. These properties allow you to manipulate the z-transform equations and solve for the unit-pulse and step response of the overall system.

I recommend reviewing your notes or textbook on the properties and equations of the z-transform. Additionally, there are many online resources and tutorials available that can help you understand and apply the z-transform to solve similar problems.

Once you have a solid understanding of the z-transform, you can start by using the given transfer functions to find the overall transfer function of the system. Then, you can use this overall transfer function to solve for the unit-pulse and step response.

I hope this helps guide you in the right direction. Remember, it's important to have a solid understanding of the concept before attempting to solve the problem. Good luck!