Generating CSD Codes from Decimal Coefficients

In digital signal processing, CSD (Canonic Signed Digit) coding is an efficient coefficient representation method that optimizes hardware implementation of filters. While MATLAB's FDATOOL can design filters and generate corresponding decimal coefficients, these coefficients typically need conversion to CSD codes to reduce multiplier count and lower hardware complexity.

First, design the filter using FDATOOL and export its decimal coefficients. These coefficients are usually floating-point numbers that require quantization to fixed-point format. The fundamental concept of CSD coding involves representing coefficients using {-1, 0, 1} values, enabling the replacement of multiplication operations with shift-and-add operations to enhance computational efficiency.

In MATLAB implementation, decimal-to-CSD conversion can be achieved through iterative algorithms. The core approach involves: normalizing coefficients first, then performing bit-by-bit comparison and adjustment to approximate the original values while minimizing non-zero bits. The algorithm typically implements a greedy search strategy that evaluates each bit position to determine optimal signed-digit representations. The converted CSD codes can be directly implemented in hardware description languages (such as Verilog or VHDL) to improve filter efficiency in FPGA or ASIC implementations.

This methodology enables significant reduction in hardware resource consumption while maintaining filter performance, making it particularly suitable for optimized implementations in high-speed digital signal processing systems.