Magnitude of Complex Exponential Polynomial Inequality

In summary, The conversation is about finding the value of b that will result in the maximum magnitude of the frequency response function, which has a complex exponential expression. The approach suggested is to first find the value of w that maximizes the expression, then use that value to calculate b as 1 divided by the magnitude of the expression. The speaker mentions their struggles with understanding this concept at the graduate level.
  • #1
eric.williams
1
0

Homework Statement



Digital filter analysis - this is just one part of a multi-part question I can't move forward with. It's supposed to be an auxilliary question and isn't the "meat" of the problem.

Find b, such that maximum of the magnitude of the frequency response function b/(1-0.8e\^{-jw}+0.81e^{-j2w}) is 1

Homework Equations


The Attempt at a Solution



I've tried decomposing real and imaginary sinusoids but I'm unsure how to use them in the absolute value function. I never had an intuitive understanding of this in undergrad, and now at the graduate level it's simply expected to be second nature.
 
Physics news on Phys.org
  • #2
first find the w that maximises the expression, then take the magnitude and b will b equal to 1 divded by that result
 

FAQ: Magnitude of Complex Exponential Polynomial Inequality

What is the magnitude of a complex exponential polynomial inequality?

The magnitude of a complex exponential polynomial inequality refers to the absolute value or magnitude of the expression on the left side of the inequality symbol. It represents the distance of the expression from zero on the number line.

How is the magnitude of a complex exponential polynomial inequality calculated?

The magnitude of a complex exponential polynomial inequality can be calculated by taking the absolute value of the entire expression on the left side of the inequality symbol. This means removing any negative signs and treating all variables as positive values.

What is the significance of the magnitude of a complex exponential polynomial inequality?

The magnitude of a complex exponential polynomial inequality is important because it determines the strength of the inequality. A larger magnitude indicates a greater difference between the two sides of the inequality, while a smaller magnitude means the difference is smaller.

How does the magnitude of a complex exponential polynomial inequality affect the solution?

The magnitude of a complex exponential polynomial inequality does not affect the solution itself, but it does affect the range of possible solutions. A larger magnitude may result in a wider range of possible solutions, while a smaller magnitude may have a narrower range of solutions.

Can the magnitude of a complex exponential polynomial inequality be negative?

No, the magnitude of a complex exponential polynomial inequality cannot be negative. The absolute value function always returns a positive value, so the magnitude of any expression will be positive or zero.

Similar threads

Solving Integrals Involving Complex Exponentials
Replies
2
Views
1K
How to write the complex exponential in terms of sine/cosine?
Replies
7
Views
4K
Trigonometric function and complex exponential
Replies
3
Views
1K
Proving various properties of complex numbers
Replies
3
Views
936
Complex Exponentials Signal processing
Replies
3
Views
1K
Integrating power of a cosine times a complex exponential
Replies
1
Views
2K
Factoring Polynomials [Abstract Algebra]
Replies
17
Views
2K
Functional Derivative of Long Range Dipole Interaction Energy
Replies
1
Views
1K
Finding Largest r in the Complex Exponential Function Mapping D(z0,r)
Replies
3
Views
2K
I Real ODE yields real solution through complex numbers
Replies
3
Views
2K

Hot Threads

Recent Insights

Back
Top