Notes on Digital Signal Processing: Practical Recipes for Design, Analysis and Implementation

Note 50. Designing IIR Filters: Impulse Invariance Method

The impulse invariance technique is based on the simple idea of obtaining an impulse response for a digital filter by sampling an analog filter’s impulse response. Recipe 50.1 provides the details for a direct implementation of this idea. However, the actual design is often carried out in the frequency domain without ever explicitly determining the impulse response of the analog prototype. The frequency-domain approach is detailed in Recipe 50.2. The mathematical justification for the frequency-domain approach can be found in [1–2].

The details of how the impulse invariance technique maps s-plane features of the analog prototype filter into z-plane features of the targeted IIR filter ...