What high school in the US gets to this level of algebra?--you're lucky if they even go to second-order exponents or polynominals. Many stop at the y = x + N level.
But besides that minor complaint, a very good article.
Other than academic curiosity, I fail to see the advantage of factoring the polynomial of the full FIR filter just to see a bunch of neat little sub-filters.
BTW Bill, it is quite common for U.S. high school students to get through a first year of calculus in high school, not to mention factoring polynomials, manipulating complex numbers and lots of other fun stuff :)
well written & fun-to-read article as always from the filter guru! So, maybe I'm just a hair-splitter, but shouldn't it read *four* nulls and *four* first order terms in the last section?
If we didn't split hairs, how would we know what's inside them (-8b
But in this instance I stand by my assertion. Check equation : it has three quadratic factors that have unity z^0, and three nulls in the stopband. I'm not counting the almost-null at Nyquist, on the grounds that 1.052235 doesn't equal unity...