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; complicates the overall processing flow. This paper addresses the convolution of high-speed 1-bit audio signals with multi-bit FIR impulse responses ; presents a systematic formulation of a multiplier-less convolution approach. Based on a mathematical reinterpretation of convolution, the proposed formulation describes how time shifting; 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; compare them with those obtained by multi-bit convolution followed by ΔΣ 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.
