Digital Signal Processing Basics
Which of the following is a correct precaution when implementing a high-order IIR filter in fixed point with coefficients of limited bit width?
- AThe poles of an IIR filter are not affected by coefficient quantization, so the coefficient bit width only needs to be chosen for passband gain accuracy
- BLike an FIR filter, it always stays stable after coefficient quantization, so even at high order it is best implemented as a single difference equation
- CImplementing the high-order denominator as a single expression lets coefficient errors move the poles and can make it unstable, so it is split into a cascade of second-order sections
Show answer and explanation
Answer: C. Implementing the high-order denominator as a single expression lets coefficient errors move the poles and can make it unstable, so it is split into a cascade of second-order sections
The roots (poles) of a high-order polynomial are sensitive to tiny changes in its coefficients; especially in steep filters whose poles cluster near the unit circle, merely rounding the coefficients can push a pole outside the unit circle. Splitting the filter into second-order sections (biquads), each handling two poles, and connecting them in cascade keeps each section's coefficient errors from affecting the other poles, making it robust to quantization. An FIR filter stays stable after coefficient quantization, although its frequency response changes.
- A. The poles of an IIR filter are set by the denominator coefficients, and quantization moves them.
- B. Only FIR filters, which have no feedback, always stay stable after quantization; IIR filters can become unstable.
- C. Correct. A cascade of second-order sections makes the pole positions robust to coefficient errors.