MatlabHmwk2F11

# MatlabHmwk2F11 - EE538 Digital Signal Processing I Due Date...

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EE538 Digital Signal Processing I Matlab Homework 2 Due Date: Friday, Nov. 18, Fall 2011 Note: You should make use of the matlab codes PR4chan.m and PRRC4chan.m posted at the course web site. Background. See relevant notes at course web site. 0 x [n] x [n] 1 H ( ϖ ) 0 8 H ( ϖ ) 1 8 H ( ϖ ) 2 8 H ( ϖ ) 3 8 H ( ϖ ) 4 8 H ( ϖ ) 5 8 H ( ϖ ) 6 8 H ( ϖ ) 7 8 x[n] x [n] 2 x [n] 3 x [n] 4 x [n] 5 x [n] 6 x [n] 7 G ( ϖ ) 7 G ( ϖ ) 6 G ( ϖ ) 5 G ( ϖ ) 4 G ( ϖ ) 3 G ( ϖ ) 2 G ( ϖ ) 1 G ( ϖ ) 0 0 x [n] x [n] 1 8 8 8 8 8 8 8 8 x [n] 2 x [n] 3 x [n] 4 x [n] 5 x [n] 6 x [n] 7 y[n] + + + + + + + Figure 1(a). Analysis Filter Bank, M = 8. Figure 1(b). Synthesis Filter Bank, M = 8. 1

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0 x [n] x [n] 1 x[n] H ( ϖ ) 1 2 (2) H ( ϖ ) 0 2 (2) H ( ϖ ) 0 2 H ( ϖ ) 1 2 (2) (2) H ( ϖ ) 0 2 H ( ϖ ) 1 2 (2) (2) H ( ϖ ) 0 2 H ( ϖ ) 1 2 (2) (2) H ( ϖ ) 0 2 H ( ϖ ) 1 2 (2) (2) H ( ϖ ) 0 2 (2) H ( ϖ ) 1 2 (2) H ( ϖ ) 0 2 (2) H ( ϖ ) 1 2 (2) x [n] 2 x [n] 3 x [n] 4 x [n] 5 x [n] 6 x [n] 7 Figure 2(a). Analysis Section of Three-Stage Tree-Structured Filter Bank. y[n] 2 G ( ϖ ) 0 (2) 2 G ( ϖ ) 1 (2) G ( ϖ ) 1 (2) G ( ϖ ) 0 (2) G ( ϖ ) 1 (2) G ( ϖ ) 0 (2) G ( ϖ ) 1 (2) G ( ϖ ) 0 (2) G ( ϖ ) 1 (2) G ( ϖ ) 0 (2) 2 G ( ϖ ) 1 (2) 2 G ( ϖ ) 0 (2) 2 G ( ϖ ) 1 (2) 2 G ( ϖ ) 0 (2) 0 x [n] x [n] 1 2 2 2 2 2 2 2 2 x [n] 2 x [n] 3 x [n] 4 x [n] 5 x [n] 6 x [n] 7 Figure 2(b). Synthesis Section of Three-Stage Tree-Structured Filter Bank. 2
Synthesizing M=8 Channel Perfect Reconstruction Filter Banks from Tree- Structured Filter Banks. This Matlab assignment is centered on synthesizing an M=8 channel uniform PR filter bank from a three stage tree-structured PR filter bank. As dis- cussed in class, if the number of channels, M , is a power of two, an M-channel uniform PR filter bank may be synthesized via an equivalent (in terms of I/O relationship) tree- structured PR filter bank having log 2 ( M ) stages with each stage formed from a two-channel QMF filter bank as depicted in Figure 2. That is, the combination of the analysis filter pair, { H

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