Sampling the Impulse Response

Sampling is elementary. Since we have defined the admittance as the nominal transfer function, corresponding to defining the input as driving force and the output as resulting velocity (see Fig.L.3), we have that is defined as the system impulse response .^R.2 We are therefore digitizing a linear system by sampling its impulse response. The model is then implemented as a Finite Impulse Response (FIR) digital filter (§1.5.4). The next subsection describes the impulse-invariant method for digital filter design which derives an infinite impulse response (IIR) digital filter that matches the analog filter impulse response at the sampling points.

Sampling the impulse response has the advantage of preserving resonant frequencies (see next section), but its big disadvantage is aliasing of the frequency response. No ``system'' is truly bandlimited. For example, even a simple