Filters in Matlab

• Filter coefficients in Matlab are specified in terms of the following general filter difference equation:
  $$a_0 y[n] = b_{0} x[n] + b_{1} x[n - 1] + b_{2} x[n - 2] \ldots - a_{1} y[n - 1] - a_{2} y[n - 2] \ldots, \hspace{0.2in} n = 0, 1, 2, \ldots$$

• In this way, a filter with difference equation $y[n] = x[n] + x[n-1]$ would be specified with feedforward coefficients $b = [1 \;1]$ and a feedback coefficient $a = 1$.

• Likewise, a filter with difference equation $y[n] = x[n] + 0.9 y[n-1]$ would be specified with a feedforward coefficient $b = 1$ and feedback coefficients $a = [1 \;{-0.9}]$.

• In Matlab, we can filter an input signal $x$ with a filter specified by coefficients $b$ and $a$ as y = filter(b, a, x).

• In Matlab, we can plot a filter's frequency response using the freqz function: freqz(b, a).