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First-Order Recursive Lowpass Filter

Figure 6: The spectral magnitude of the first-order FIR and IIR (recursive) lowpass filters.
\scalebox{0.7}{\includegraphics{eps/simpiir.eps}}

The general difference equation for LTI filters therefore, includes feedback terms, and is given by

$\displaystyle y(n) = b_0x(n)$ $\displaystyle +$ $\displaystyle b_1x(n-1) + \cdots + b_Mx(n-m)$  
  $\displaystyle -$ $\displaystyle a_1y(n-1) - \cdots - a_Ny(n-N)$  

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``Music 171: Introduction to Delay and Filters'' by Tamara Smyth, Computing Science, Simon Fraser University.
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Copyright © 2019-03-07 by Tamara Smyth.
Please email errata, comments, and suggestions to Tamara Smyth<trsmyth@ucsd.edu>