Inverse Z Transform Of Signal With Complex Conjugate Poles (Problems) - Z Transform

TL;DR

Learn how to find the inverse z-transform of signals with complex conjugate poles and numerator degree greater than denominator.

Transcript

click the bell icon to get latest videos from equator hello friends and today we are going to study a new topic in which we are going to study inverse z-transform of signals with the complex conjugate poles and when numerator degree is greater than denominator here we are going to show you two different topics first one is signals with complex conj... Read More

Key Insights

• 💈 Signals with complex conjugate poles exhibit a sinusoidal behavior due to the presence of imaginary parts in the poles.
• 🇨🇬 The poles of a function can be calculated using the formula -B ± √(B² - 4AC) / 2A, where A, B, and C are the coefficients of the highest power, Z inverse, and Z to the power -2 in the denominator, respectively.
• 🤪 The partial fraction method is used to find the constants in the inverse z-transform calculation.
• 💤 Multiplying the numerator and denominator by Z² helps in converting the Z inverse terms to a positive power of Z, simplifying the partial fraction calculation.
• 🥳 The complex conjugate values of the poles have the same real part and different imaginary parts.
• 😄 Polar form representation of constants in the inverse z-transform allows for ease of calculation and manipulation.
• 🤪 Understanding how to factorize the denominator and solve for the constants is essential in finding the inverse z-transform of signals with complex conjugate poles.

Questions & Answers

Q: How do you calculate the poles of a function with complex conjugate poles?

To calculate the poles, you can use the formula -B ± √(B² - 4AC) / 2A, where A, B, and C are the coefficients of the highest power, Z inverse, and Z to the power -2 in the denominator, respectively.

Q: What is the significance of complex conjugate poles?

Complex conjugate poles have the same real part and different imaginary parts. They play a crucial role in determining the behavior and stability of a system.

Q: How do you find the constants in the partial fraction method?

You can find the constants by substituting the complex conjugate values of the poles into the given function and solving the resulting equations simultaneously.

Q: Why do we multiply the numerator and denominator by Z² in the process?

Multiplying by Z² allows us to convert the Z inverse terms in the function to a positive power of Z, simplifying the calculation of partial fractions.

Summary & Key Takeaways

• The video discusses finding the inverse z-transform of signals with complex conjugate poles and when the numerator degree is greater than the denominator.

• The content includes three numerical examples based on signals with complex conjugate poles and three examples with numerator degrees greater than denominator.

• The video explains how to calculate the poles of the function and how to use the partial fraction method to find the constant values.

• It demonstrates the step-by-step process of finding the inverse z-transform using the given numericals.