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simpler way to get a particular banded matrix?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg98079] simpler way to get a particular banded matrix?
  • From: rip pelletier <bitbucket at comcast.net>
  • Date: Sun, 29 Mar 2009 02:48:12 -0500 (EST)

Hi,

The following command constructs a matrix (typically denoted M0, it 
arises in filter banks in general, in Burrus, Gopinath, & Guo "intro to 
wavelets and wavelet transforms: a primer" in particular).

I'm sure there's a way to do this without typing out all 5 bands. Here's 
what i did:

SparseArray[Band[{1,1}]->H,{6,6}]+
SparseArray[Band[{2,3}]->H,{6,6}]+
SparseArray[Band[{3,5}]->H,{6,6}]+
SparseArray[Band[{-2,-3},{1,1},{-1,-1}]->rH,{6,6}]+
SparseArray[Band[{-3,-5},{1,1},{-1,-1}]->rH,{6,6}]

where

H={h0,h1,h2,h3,h4,h5};
rH=Reverse[H];

I get what I want:

h0  0  0  0  0  0
h2 h1 h0 0  0  0
h4 h3 h2 h1 h0 0
0  h5 h4 h3 h2 h1
0  0  0  h5 h4 h3
0  0  0  0  0  h5

Any easier ways to get this?

TIA and vale,
   rip

-- 
NB eddress is r i p 1 AT c o m c a s t DOT n e t


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