Next  |  Prev  |  Top  |  REALSIMPLE Top

General Causal FIR Filters

The most general case of a TDL having a tap after every delay element is the general causal finite impulse response (FIR) filter,

\begin{figure}\centering
\input fig/fir.pstex_t
\\ {\LARGE }
\end{figure}

Difference Equation:

$\displaystyle y(n) = b_0 x(n) + b_1 x(n-1) + b_2 x(n-2) + b_3 x(n-3) + \cdots + b_M x(n-M)
$

Transfer Function:

$\displaystyle H(z) = b_0 + b_1 z^{-1} + b_2 z^{-2} + b_3 z^{-3} + \cdots + b_M z^{-M}
= \sum_{m=0}^M b_m z^{-m} \mathrel{\stackrel{\Delta}{=}}B(z)
$


Next  |  Prev  |  Top  |  REALSIMPLE Top

Download Delay.pdf
Download Delay_2up.pdf
Download Delay_4up.pdf

``Computational Acoustic Modeling with Digital Delay'', by Julius O. Smith III and Nelson Lee,
REALSIMPLE Project — work supported by the Wallenberg Global Learning Network .
Released 2008-06-05 under the Creative Commons License (Attribution 2.5), by Julius O. Smith III and Nelson Lee
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University
CCRMA