What I don't understand about this algorithm-:

  1. What is the diffeence between w and w cap?

  2. What is the meaning of extremals?

  3. What does it means to reject p-r superfluous potential...

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  • $\begingroup$ hm, that involves solving systems of equations with many unknowns, which is why it's a numerical algorithm and not something you do by hand. What kind of example do you hope for, and how would it differ from the text that you just posted? $\endgroup$ Aug 3 '21 at 15:17
  • $\begingroup$ Ah sorry, I don't need an example. I edited the post. I just need the explanation of few questions I had above. My teacher has also told me to memorize this algorithm and write in exam. $\endgroup$
    – broman
    Aug 3 '21 at 15:20
  • $\begingroup$ OK; so re: 2. "extremals" are.. extremals, there's a wikipedia article of "Extremal". Re: 3. Probably defined just half a page before. Re 1.: well, $\omega$ is a variable, and $\overset\frown\omega$ are specific values for $\omega$ as defined in the text you pasted. $\endgroup$ Aug 3 '21 at 15:22

Not sure if this helps or not: it's another explanation of the Remez algorithm specifically for the Parks-McClellan algorithm.

Answers to your explicit questions:

  1. $\hat{\omega}_k$ are specific frequencies and $\omega$ is a variable.

  2. The extremals are the peaks of the error function (called norm-points below).

  3. For an optimal filter, you only need $r+1$ extremals. The algorithm you state will give more. It's saying to ignore the ones you don't need to find the answer.

Kootsookos's explanation


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