Near-optimal Multiplier-Less Broadband Noise Shaping Filters

Noise shaping (NS) filters reduce the quantization noise power in one or more frequency band(s) while amplifying it in other bands. Narrow-band noise shaping filters are state of the art in audio signal processing, analog-digital and digital-analog conversion, direct digital synthesis, and other applications. However, it is much more difficult to design broadband NS filters. Since NS filters are used in feedback branches, they must therefore be designed direct path free which imposes a constraint on the filter coefficients. This constraint leads to prohibitive large filter coefficients employing state of the art filter design techniques. This paper investigates the theoretical bound for NS filters and shows results about a novel design method for broadband FIR and IIR noise shaping filters and its multiplier-less hardware implementation. The method employed is a purely numerical approximation technique and leads to filter designs close to the discussed theoretical bound. The quantization of the filter coefficients is performed by a Canonical Signed Digit (CSD) representation of the coefficients. Two alternative architectures for the implementation of the filters are discussed. The design technique and the CSD quantization are realized in a MATLAB toolbox. The filters were moreover implemented in VHDL.