ROC in Z-Transform Problem 05 | Z-Transform | Signals and System

TL;DR

In this video, the problem of determining the Z-transform and ROC (Region of Convergence) for a given sample sequence is solved.

Transcript

click the bell icon to get latest videos from equator hello friends and today we're going to study a numerical number 5 that is problem number 5 based on ROC in Z transform so first of all let's go through the question and then we'll move on to solution determine zip transform and also find it ROC where the sample value is 0 now look at here the ar... Read More

Key Insights

• 📌 The location of the origin helps determine the instance values and amplitudes of the sample sequence.
• 🤪 The Z-transform is calculated by applying the definition using the given values.
• 💤 The ROC of X(Z) is determined by converting the negative powers of Z into positive.

Questions & Answers

Q: What is the problem being discussed in the video?

The video discusses a numerical problem related to determining the Z-transform and ROC for a given sample sequence.

Q: How is the location of the origin relevant to the problem?

The location of the origin is important for determining the amplitudes of the sample instances. The samples to the right of the origin have positive instance values.

Q: What is the definition of Z-transform used in the solution?

The Z-transform is represented by X(Z) and its definition includes a summation of values of the sequence multiplied by Z to the power of the negative instance value.

Q: How is the ROC of X(Z) determined?

The ROC of X(Z) is determined by converting the negative powers of Z into positive by taking the reciprocal. The ROC is found to be the entire region of the Z-plane excluding Z=0.

Summary & Key Takeaways

• The video discusses a numerical problem based on ROC in Z transform.

• The problem involves determining the Z-transform and ROC for a sample sequence when the sample value is 0.

• The solution includes finding the amplitude values at different sample instances and applying the definition of Z-transform.

• The final result is the Z-transform of the given sample sequence and the ROC is determined to be the entire region of the Z-plane excluding Z=0.