Why IIR Filters Become Unstable in Fixed-Point DSP Systems
Introduction Infinite Impulse Response (IIR) filters are the workhorses of real-time DSP systems. They offer superior frequency selectivity with fewer coefficients compared to FIR filters, making them ideal for resource-constrained embedded applications. However, every DSP engineer who has implemented IIR filters in fixed-point systems has encountered the dreaded instability: filters that work perfectly in floating-point simulation suddenly oscillate, saturate, or produce garbage output when deployed to hardware. This isn’t just academic—it’s a production-stopping problem that has derailed countless projects. The issue stems from the fundamental tension between IIR filters’ recursive nature and the limited precision of fixed-point arithmetic. In this article, we’ll dissect exactly why this happens and provide practical solutions you can implement today. ...