Near-optimal Multiplier-Less Broadband Noise Shaping Filters

Hans Georg Brachtendorf, Christoph Dalpiaz

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Article number8
Pages (from-to)991-1002
Number of pages12
JournalJournal of Signal Processing Systems
Issue number8
Publication statusPublished - 1 Aug 2023


  • Broadband Noise Shaping Filters (NSF)
  • Canonical Signed Digit (CSD)
  • Multiplier-less NSF
  • Near-optimal design
  • Seemless design flow
  • VHDL implementation


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