Cost-efficient multiplier-less FIR filter structure based on modified DECOR transformation

We propose a new design approach to implement an FIR filter using canonical sign digit (CSD) multipliers based on modified decorrelating transformation (MDECOR). The direct CSD approach will introduce serious quantization errors since the distribution of CSD numbers is very non-uniform. The proposed MDECOR transformation provides a systematic solution to reduce the dynamic range effectively. By combining the proposed MDECOR transformation followed by CSD quantization, we can avoid the aforementioned quantization problem. As a result, we do not need to employ additional non-zero bits to compensate for the distortion caused by direct CSD quantization, which helps to save the number of adders in VLSI implementations. Furthermore, the MDECOR transformation offers more freedom in the filter design. It can achieve high-precision performance under the same hardware complexity as the direct CSD approach. Our simulation results show that we can save 20% of the number of adders compared with the direct CSD approach