Network function. 6th degree polynomial to complex numbers

In summary, the conversation was about obtaining a transfer function from its squared magnitude and understanding how a 6th degree polynomial was broken down into equations involving complex numbers. The person asking the question mentioned using software like MATLAB to find the zeros of the polynomial, but was seeking clarification on how to do it manually on paper.
  • #1
nearxos
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Homework Statement



the problem that i attached bellow is related to how you can obtain a transfer function from its squared magnituded.

my question is not on the problem it self as its just a solved example from my book.
what i find difficult to understand as you can see from my attachment is how the 6th degree polynomial was break down to equations that involves complex number.
 

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  • #2
You could easily find the six zeros of the polynomial in the denominator using software such as MATLAB and then write it as a product of its factors, given that (s-k) is a factor of a polynomial f(s) if and only if f(k)=0
 
  • #3
I know how to solve it with matlab. But I need to know how I can do it on paper.

Thanks for the reply
 

Related to Network function. 6th degree polynomial to complex numbers

1. What is network function?

Network function refers to the mathematical representation of a network or system, which describes its input-output relationship. It helps in analyzing and understanding the behavior of a network and predicting its response to certain inputs.

2. What is a 6th degree polynomial?

A 6th degree polynomial is a mathematical expression that contains a variable raised to the power of six, along with other terms and coefficients. It can be written in the form of ax^6 + bx^5 + cx^4 + dx^3 + ex^2 + fx + g, where a, b, c, d, e, f, and g are constants.

3. What are complex numbers?

Complex numbers are numbers that can be expressed in the form of a + bi, where a and b are real numbers and i is the imaginary unit (√-1). They are used to represent both real and imaginary quantities, and are an important tool in mathematics and engineering.

4. How do you represent a 6th degree polynomial in terms of complex numbers?

A 6th degree polynomial can be represented in terms of complex numbers by factoring it into linear and quadratic terms. This allows for the use of the quadratic formula to find the roots of the polynomial, which can then be expressed in terms of complex numbers.

5. What is the significance of using complex numbers in network function analysis?

Complex numbers are used in network function analysis to represent the frequency response of a system. By converting a 6th degree polynomial to complex numbers, we can analyze the behavior of the system at different frequencies, which is crucial in designing and optimizing networks for specific applications.

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