Various AD conversion methods exist, and high-speed 1 bit method have been proposed with using a high sampling frequency and 1 bit quantization. The ΔΣ modulation is mainly used, and due to its characteristic, these signals are able to accurately preserve the spectrum of the analog signal and move quantization noise into higher frequency bands, which allows for a high signal-to-noise ratio in the audible range. However, when performing signal processing tasks such as addition and multiplication on high-speed 1 bit signals, it is generally necessary to convert them into multi-bit signals for arithmetic operations. In this paper, we propose a direct processing method for high-speed 1 bit signal without converting them into multi-bit signal and the convolution is realized. In this method, 1 bit data are reordered to achieve operations without arithmetic one. The proposed method was verified through the simulations with using low-pass FIR filters. Frequency-domain analysis showed that the proposed method achieved equivalent performance to conventional multi-bit convolutions with successfully performing the desired filtering. We present a novel approach to directly processing high-speed 1 bit signals and suggest potential applications in audio and signal processing fields.
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