ROC in Z-Transform Problem 03 | Z-Transform | Signals and System | Summary and Q&A

TL;DR

Determining the Z transform and ROC for a given signal using ROC in Z transform.

Key Insights

• 🤪 The Z transform and ROC are essential tools in analyzing the properties and behavior of a discrete signal.
• 🤪 The Z transform is calculated using the formula Z^(-n) by substituting the amplitude values of the given signal.
• 😥 The ROC is determined at specific points, such as Z=0 and Z=infinity, to understand the infinite or finite behavior of the signal.

Transcript

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Questions & Answers

Q: What is the purpose of determining the Z transform and ROC?

The Z transform and ROC help in analyzing and understanding the properties and behavior of a given discrete signal in terms of its frequency response and stability.

Q: How are the amplitude values of the given signal identified?

The amplitude values of the signal are given as discrete samples, and arrows are used to indicate the location of each amplitude value on the Z plane.

Q: What is the formula used to calculate the Z transform?

The formula for the Z transform is Z^(-n), where n represents the sample position or index of the given signal.

Q: How are the values substituted in the Z transform formula to calculate the Z transform?

The values of each sample in the given signal, both positive and negative instances, are substituted into the Z transform formula to calculate the Z transform for the entire sequence.

Summary & Key Takeaways

• The content focuses on solving the problem of determining the Z transform and ROC of a given signal using ROC in Z transform.

• The signal or sequence provided has amplitude values ranging from -2 to +2.

• The Z transform is calculated using the formula Z^(-n) and the ROC is determined at Z=0 and Z=infinity.