Spectral Factorization for Non-Polynomial Equations

In summary, the conversation is about spectral factorization when the equation is not in terms of a polynomial of f. The person is struggling with finding resources on this topic and is wondering if they need to use convolution in the frequency domain, but is concerned about the possibility of division by zero. They express hope that they can find another method to avoid this issue.
  • #1
RoshanBBQ
280
0

Homework Statement


I have [tex]\frac{5}{4}s_x(f)+s_x(f)cos(2\pi f t_0) + 10[/tex]
where s_x is 2 between f = -10khz to 10 khz else zero (a rectangle).

How do I do spectral factorization when the equation is not in terms of a polynomial of f? All material I can find on this topic have the thing needing to be factorized conveniently in a polynomial of f.

Do I have to do convolution in the frequency domain to represent the multiplication of a unit step in the time domain? If so, the tau = 0 case results in division by zero, and that seems really messy. Let's hope I can avoid that method.
 
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  • #2
Homework EquationsNo equations. Just need help with the factorization.The Attempt at a SolutionI'm sorry, I'm stuck.
 

FAQ: Spectral Factorization for Non-Polynomial Equations

What is spectral factorization?

Spectral factorization is a mathematical process that decomposes a signal or system into its constituent frequencies. It is commonly used in signal processing and control systems engineering.

2. Why is spectral factorization important?

Spectral factorization allows us to understand the frequency components of a signal or system, which can provide insights into its behavior and help with tasks such as filtering, noise reduction, and control.

3. How is spectral factorization performed?

Spectral factorization is typically performed using methods such as the Cholesky decomposition, eigenvalue decomposition, or singular value decomposition. These methods involve manipulating matrices to extract the frequency components of the signal or system.

4. What are some applications of spectral factorization?

Spectral factorization has many applications, including in audio and image processing, control systems, and data analysis. It is also used in fields such as telecommunications, geophysics, and biomedical engineering.

5. Are there any limitations to spectral factorization?

While spectral factorization is a powerful tool, it does have some limitations. It assumes that the signal or system can be represented as a linear combination of frequencies, so it may not be suitable for complex nonlinear systems. It also requires accurate and complete data to produce meaningful results.

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