Inverse Z Transform Concepts

The video tutorial explains the inverse Z transform using the long division method, also known as the power series expansion method. It covers the conditions for Z transform, such as mod z > 1 and mod z < 1, and discusses the concepts of causal and anti-causal systems. The tutorial details the process of converting negative powers to positive powers and emphasizes the importance of descending order for causal systems. The division process is demonstrated step-by-step, leading to the final results of the inverse Z transform.

What method is used to learn the inverse Z transform in this video?

• Long division method

• Fourier transform method

• Matrix inversion method

• Laplace transform method

What are the two conditions given for the inverse Z transform?

• mod z equal to one and mod z not equal to one

• mod z greater than one and mod z less than one

• mod z greater than zero and mod z less than zero

• mod z equal to zero and mod z not equal to zero

What does the unit circle represent in the context of the inverse Z transform?

• A circle with radius 2

• A circle with radius 1

• A circle with radius 0.5

• A circle with radius 3

What is the significance of the unit circle in the inverse Z transform?

• It represents the center of the system

• It represents the exterior of the system

• It represents the boundary of the system

• It represents the interior of the system

What is the difference between causal and anti-causal systems?

• Causal systems are inside the unit circle, anti-causal are outside

• Causal systems are neither inside nor outside the unit circle

• Causal systems are outside the unit circle, anti-causal are inside

• Causal systems are on the unit circle, anti-causal are not

What does a positive power indicate in the context of the inverse Z transform?

• A power equal to zero

• A power less than zero

• A power not equal to zero

• A power greater than zero

How are negative powers converted to positive powers in the inverse Z transform?

• By subtracting 1 from the power

• By taking the reciprocal

• By multiplying by zero

• By adding 1 to the power

What is the first step in the division process for the causal system?

• Divide all terms by zero

• Convert all powers to negative

• Convert all powers to positive

• Multiply all terms by zero

What pattern is observed in the division process?

• The powers alternate between positive and negative

• The powers remain constant

• The powers decrease by 1

• The powers increase by 1

What formula is used to find the inverse Z transform?

• Summation of n equal to 0 to infinity of x of n z power minus n

• Summation of n equal to 1 to infinity of x of n z power minus n

• Summation of n equal to 1 to infinity of x of n z power n

• Summation of n equal to 0 to infinity of x of n z power n