High-Accuracy and Low-Multiplication Recursive Discrete Cosine Transform Algorithm Design and Its Realization in Mel-Scale Frequency Cepstral Coefficients

Abstract

This brief introduces an innovative recursive discrete cosine transform (DCT) algorithm characterized by its exceptional precision and minimal multiplication requirements. Through the strategic implementation of data reordering and “q” value adjustment schemes, the proposed algorithm entails only a single constant-multiplication operation featuring a fixed cosine coefficient within the iterative phase. By judiciously selecting an appropriate “q” value (q =41), it achieves outstanding results, reaching peak signal-to-noise ratios (PSNRs) of 94.9 and 100.9 dB under 18-bit and 20-bit word length (WL) conditions, respectively, in terms of decimal places. Notably, the proposed algorithm substantially diminishes the number of multiplications by 86.08%, offset by an increase of 2688 additions. The proposed design has a simpler structure and utilizes fewer hardware resources. In field programmable gate array (FPGA) implementation, the device is composed of 43 combinational adaptive look-up tables (ALUTs) specifically allocated for constant multiplication (CM). Overall, the proposed accelerator totally takes 158 combinational ALUTs, 65 registers, a 960-bit read-only memory (ROM), and a 1024-bit random access memory (RAM) in hardware realization and can be operated at a maximum frequency of 156.62 MHz. Therefore, it is particularly well-suited for VLSI implementation in a parallel calculation of Mel-scale frequency cepstral coefficients (MFCCs).