Sign in

username:

password:



Not a member?

Search Online Books



Search tips

Free Online Books

Ads

Chapters

Introduction to Digital Filters
    Transfer Function Analysis
       Partial Fraction Expansion
          Software for Partial Fraction Expansion
             Example 2

Chapter Contents:

Search Introduction to Digital Filters

  

Book Index | Global Index

Would you like to be notified by email when Julius Orion Smith III publishes a new entry into his blog?

  

Example 2

For the filter

$\displaystyle H(z)$ $\displaystyle \isdef$ $\displaystyle \frac{2+6z^{-1}+6z^{-2}+2z^{-3}}{1-2z^{-1}+z^{-2}}$ (7.20)
  $\displaystyle =$ $\displaystyle (2+10z^{-1}) + z^{-2}\left[\frac{8}{1-z^{-1}} + \frac{16}{(1-z^{-1})^2}\right] \protect$ (7.21)

we obtain the output of residued (§J.6) shown in Fig.6.4. In contrast to residuez, residued delays the IIR part until after the FIR part. In contrast to this result, residuez returns r=[-24;16] and f=[10;2], corresponding to the PFE

$\displaystyle H(z) = 10+2z^{-1}-\frac{24}{1-z^{-1}} + \frac{16}{(1-z^{-1})^2},$ (7.22)

in which the FIR and IIR parts have overlapping impulse responses.

See Sections J.5 and J.6 starting on page [*] for listings of residuez, residued and related discussion.

Figure 6.4: Use of residued to perform a partial fraction expansion of an IIR filter transfer function $ H(z)=B(z)/A(z)$.
  
B=[2 6 6 2]; A=[1 -2 1];
[r,p,f,m] = residued(B,A)
% r =
%    8
%   16
% 
% p =
%   1
%   1
% 
% f =
%    2  10
% 
% m =
%   1
%   2

Order a Hardcopy of Introduction to Digital Filters

Previous: Software for Partial Fraction Expansion
Next: Polynomial Multiplication in Matlab
written by Julius Orion Smith III
Julius Smith's background is in electrical engineering (BS Rice 1975, PhD Stanford 1983). He is presently Professor of Music and Associate Professor (by courtesy) of Electrical Engineering at Stanford's Center for Computer Research in Music and Acoustics (CCRMA), teaching courses and pursuing research related to signal processing applied to music and audio systems. See http://ccrma.stanford.edu/~jos/ for details.


Comments

No comments yet for this page


Add a Comment
You need to login before you can post a comment (best way to prevent spam). ( Not a member? )