Magnitude of Complex Exponential Polynomial Inequality

  • #1

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.
 

Answers and Replies

  • #2
lanedance
Homework Helper
3,304
2
first find the w that maximises the expression, then take the magnitude and b will b equal to 1 divded by that result
 

Related Threads on Magnitude of Complex Exponential Polynomial Inequality

  • Last Post
Replies
8
Views
4K
  • Last Post
Replies
8
Views
1K
  • Last Post
Replies
6
Views
1K
Replies
1
Views
749
  • Last Post
Replies
2
Views
3K
  • Last Post
Replies
7
Views
1K
  • Last Post
Replies
4
Views
1K
  • Last Post
Replies
1
Views
609
  • Last Post
Replies
5
Views
1K
Top