Systematization of Multiplier-less Convolution for 1-bit Audio Signal

Gomi Y, Sakurai I, Sakaguchi T, Oikawa Y. Systematization of Multiplier-less Convolution for 1-bit Audio Signal. In: Convention Paper. Audio Engineering Society; 2026. Paper 10299. Available from: https://aes.org/publications/elibrary-page/?id=23193

@inproceedings{Gomi2026_23193,
  author = {Gomi, Yuta and Sakurai, Iori and Sakaguchi, Tomohiro and Oikawa, Yasuhiro},
  title = {{Systematization of Multiplier-less Convolution for 1-bit Audio Signal}},
  note = {Paper 10299},
  year = {2026},
  month = may,
  publisher = {Audio Engineering Society},
  url = {https://aes.org/publications/elibrary-page/?id=23193}
}

TY  - CPAPER
TI  - Systematization of Multiplier-less Convolution for 1-bit Audio Signal
AU  - Gomi, Yuta
AU  - Sakurai, Iori
AU  - Sakaguchi, Tomohiro
AU  - Oikawa, Yasuhiro
M1  - Paper 10299
PY  - 2026
DA  - 2026/05/28
UR  - https://aes.org/publications/elibrary-page/?id=23193
PB  - Audio Engineering Society
LA  - en
AB  - High-speed 1-bit signals generated by oversampling are widely used in audio applications as they allow simple demodulation via low-pass filtering while preserving in-band spectral characteristics with high accuracy. However, conventional FIR filtering of such signals generally requires conversion to a multi-bit representation at a common sampling frequency, which increases computational cost and complicates the overall processing flow. This paper addresses the convolution of high-speed 1-bit audio signals with multi-bit FIR impulse responses and presents a systematic formulation of a multiplier-less convolution approach. Based on a mathematical reinterpretation of convolution, the proposed formulation describes how time shifting and amplitude weighting can be expressed through structured rearranging of 1-bit samples without arithmetic operations. This provides a theoretical description of previously reported 1-bit convolution methods; however, its validity has not been fully formalized. We examine the spectral characteristics of the proposed convolution method and compare them with those obtained by multi-bit convolution followed by DS modulation. Experiments are conducted by convolving 1-bit input signals with FIR filters having multi-band frequency responses. Spectral analysis shows that the proposed method achieves extremely high agreement with the standard approach within the audible band while the differences appear primarily at much higher frequencies outside the audible range. These results demonstrate that convolution of high-speed 1-bit audio signals can be achieved without multipliers, suggesting the potential for highly efficient hardware-oriented signal processing architectures.
ER  -