8.10 Coefficient Accuracy Effects on Infinite Impulse Response Filters

In practical applications, the IIR filter coefficients with infinite precision may be quantized due to the finite word length. Quantization of infinite precision filter coefficients changes the locations of the zeros and poles of the designed filter transfer function, hence changes the filter frequency responses. Since analysis of filter coefficient quantization for the IIR filter is very complicated and beyond the scope of this textbook, we pick only a couple of simple cases for discussion. Filter coefficient quantization for specific processors such as the fixed-point DSP processor and floating-point processor will be included in Chapter 9. To illustrate this effect, we look at the following first-order IIR filter transfer function having filter coefficients with infinite precision,

(8.57)

After filter coefficient quantization, we have the quantized digital IIR filter transfer function

(8.58)

Solving for pole and zero, we achieve

(8.59)

(8.60)

Now considering a second-order IIR filter transfer function as

(8.61)

and its quantized IIR filter transfer function

(8.62)

solving for poles and zeros finds:

(8.63)

(8.64)

With the developed Equations (8.59) and (8.60) for the first-order IIR filter, and Equations (8.63) and (8.64) for the second-order IIR filter, we can study the effects of the location changes of the poles and zeros, and the frequency responses due to filter coefficient quantization.

Example 8.24.

Given the following first-order IIR filter,

and assuming that we use 1 sign bit and 6 bits for encoding the magnitude of the filter coefficients,

1. Find the quantized...