Date: Wed, 28 Apr 1999 15:07:29 -0500 <br>
To: ee648on, ee648off <br>
From: Tom Krauss <krauss@ecn.purdue.edu> <br>
Subject: Note on Homework 7, part (d) <br>
 <br>
At 2:41 PM -0500 4/26/99, Iraj Manocheri wrote: <br>
>Dear Professor, <br>
> <br>
>There is similar problem with homework 7 as was with homework 6 for Part D. <br>
>In this case complex data is used for the impulse response of the QMF <br>
>filters. <br>
>In problem 6 perfect reconstruction was possible if only the imaginary part <br>
>of the <br>
>filter output was considered. In problem 7 with M = 4, there seems to be no <br>
>perfect <br>
>reconstruction for y complex, y real, or y imaginary. <br>
> <br>
>Please give me some explanation of the reason and under what circumstances <br>
>is <br>
>PR possible. <br>
 <br>
Many of us have been asking this question and with the help <br>
of some students (I heard of a fix from Terry Charbonneau  <br>
who apparently got help from another student), I have  <br>
figured out the problem. <br>
 <br>
The issue with part (d) (in both homework 6 and this one) is <br>
that the 2 channel QMF bank with h0 = [1 j], h1 = [1 -j], <br>
g0 = [1 j], g1 = [-1 j] does NOT give simple perfect reconstruction, <br>
rather it gives  <br>
   y[n] = 2j * x[n-1] <br>
 <br>
We can remove this j factor by dividing it out in the g0 and <br>
g1, so that g0 = -j*h0 and g1 = j*h1. <br>
 <br>
When we do so, the resulting nonuniform filter bank becomes perfect <br>
reconstruction. <br>
 <br>
Regards, <br>
  Tom <br>
 <br>
PS    I noticed in Zoltowski's code PRNonuniform <br>
you need to change TWO lines to make the fix: <br>
   g0=-j*h00;  g1=j*h11;  <--- redefine g0,g1 <br>
   ... <br>
   g3=j*h11; <--- also redefine g3.   <br>
 <br>