Controlled Rounding in Low Noise Digital Filter Structures

Abstract

Several IIR digital filter structures are known which exhibit freedom of limit cycles with magnitude truncation (MT) as rounding mechanism. Other well-known structures provide low noise properties with respect to quantization. Often, nonlinear stability and quantization noise reduction are incompatible. Integrator-based structures, for example, which are common for narrowband lowpass filter applications, show an excellent low noise behaviour but they are not free from limit cycles. With controlled rounding (CR), the direction of quantization is made dependent on some suitably chosen control signal within the structure. Such a quantization mechanism has been shown to stabilize the direct form structure [1] and is easy to implement: simply subtract the control signal from the signal to be quantized, truncate the difference (MT), and subsequently add the control signal. The more difficult part is to find a suitable control signal. This contribution describes how controlled rounding can be..