April 2008
Intermediate
832 pages
26h 2m
English
Content preview from Adaptive Filters
Become an O’Reilly member and get unlimited access to this title plus top books and audiobooks from O’Reilly and nearly 200 top publishers, thousands of courses curated by job role, 150+ live events each month,
O’Reilly covers everything we've got, with content to help us build a world-class technology community, upgrade the capabilities and competencies of our teams, and improve overall team performance as well as their engagement.I wanted to learn C and C++, but it didn't click for me until I picked up an O'Reilly book. When I went on the O’Reilly platform, I was astonished to find all the books there, plus live events and sandboxes so you could play around with the technology.I’ve been on the O’Reilly platform for more than eight years. I use a couple of learning platforms, but I'm on O'Reilly more than anybody else. When you're there, you start learning. I'm never disappointed.I'm always learning. So when I got on to O'Reilly, I was like a kid in a candy store. There are playlists. There are answers. There's on-demand training. It's worth its weight in gold, in terms of what it allows me to do.
Problems and Computer Projects
PROBLEMS
Problem III.1 (Multiple Step-Sizes) Refer to expression (8.18) and choose the matrix B as B = diag{b(l), b(2),…, b(M)} with b(i) > 0. In this case, the recursion (8.20) is replaced by wi = wi–1 + μB[Rdu – Ruwi–1]. This scheme associates one step-size with each entry of the weight vector Wi. Follow the discussion in Sec. 8.2 and derive a necessary and sufficient condition on μ in order to guarantee convergence of wi to 
.
Problem III.2 (Product of infinitely many numbers) Consider a scalar recursion of the form x(i) = a(i)x(i – 1) for i ≥ 0, and assume a(i) = e−1/(i+1)2.
- (a) Verify that 0 < a(i) < 1 for all finite i.
- (b) Let
Show that p(i) converges to 
, which is a finite positive number. Hint: The series 
converges to π2/6.
Problem III.3 (Optimal Step-Size) Refer to expression (9.16) for the optimal step-size. Verify that it is equivalent to the following:
in terms of the squared Euclidean norm of the gradient vector in the numerator, and the ...
Become an O’Reilly member and get unlimited access to this title plus top books and audiobooks from O’Reilly and nearly 200 top publishers, thousands of courses curated by job role, 150+ live events each month,
and much more.
Read now
Unlock full access
More than 5,000 organizations count on O’Reilly
O’Reilly covers everything we've got, with content to help us build a world-class technology community, upgrade the capabilities and competencies of our teams, and improve overall team performance as well as their engagement.Julian F.
I wanted to learn C and C++, but it didn't click for me until I picked up an O'Reilly book. When I went on the O’Reilly platform, I was astonished to find all the books there, plus live events and sandboxes so you could play around with the technology.Addison B.
I’ve been on the O’Reilly platform for more than eight years. I use a couple of learning platforms, but I'm on O'Reilly more than anybody else. When you're there, you start learning. I'm never disappointed.Amir M.
I'm always learning. So when I got on to O'Reilly, I was like a kid in a candy store. There are playlists. There are answers. There's on-demand training. It's worth its weight in gold, in terms of what it allows me to do.