IVT Conjugate Poles | Z-Transform in Signals and Systems | Problem 1

TL;DR

This video explains how to find the inverse Z-transform of signals with complex conjugate poles and when the numerator degree is greater than the denominator.

Transcript

click the bell icon to get latest videos from ekeeda 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 study two different topics first one is signals with complex conjugat... Read More

Key Insights

• 🤪 The inverse Z-transform can be calculated using the partial fraction method for functions with complex conjugate poles.
• 🤘 Complex conjugate poles have the same real part and complex part but with opposite signs.
• 💈 The discriminant of the pole calculation formula determines whether the poles will be real or complex.
• 🖐️ Complex conjugate poles play a crucial role in solving problems involving signals with numerator degrees greater than the denominator.

Questions & Answers

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

The poles of a function can be calculated using the formula: (-b ± √(b^2 - 4ac))/2a, where the coefficients a, b, and c correspond to the powers of z in the denominator.

Q: What is the significance of complex conjugate poles?

Complex conjugate poles have the same real part and complex part but with opposite signs. They occur when the discriminant of the pole calculation formula is negative.

Q: How do you find the constants in the partial fraction method for inverse Z-transform?

By substituting the complex conjugate pole values into the function, two equations are obtained. Solving these equations will yield the constants a and b, which are complex conjugates.

Q: How can the inverse Z-transform be simplified for complex conjugate poles?

The inverse Z-transform of the function with complex conjugate poles can be simplified using the formula a^n*cos(nθ)u(n) + b^nsin(nθ)*u(n), where a and b are constants, n is the sample index, θ is the complex argument, and u(n) is the unit step function.

Summary & Key Takeaways

• This video discusses two topics: signals with complex conjugate poles and signals with numerator degree greater than the denominator.

• The first problem involves finding the inverse Z-transform of a function with a complex conjugate pole.

• The video explains how to factorize the denominator and calculate the poles of the function.

• The partial fraction method is used to solve for the constants in the inverse Z-transform.