Fast Computation of LSP Frequencies Using the Bairstow Method

• Published in: Electronics (Basel) 2020-03, Vol.9 (3), p.387
• Main Authors: Xue, Yuqun, Zhu, Zhijiu, Jiang, Jianhua, Zhan, Yi, Yu, Zenghui, Fan, Xiaohua, Qiao, Shushan
• Format: Article
• Language: English
• ISSN: 2079-9292; 2079-9292
• DOI: 10.3390/electronics9030387

Linear prediction is the kernel technology in speech processing. It has been widely applied in speech recognition, synthesis, and coding, and can efficiently and correctly represent the speech frequency spectrum with only a few parameters. Line Spectrum Pairs (LSPs) frequencies, as an alternative representation of Linear Predictive Coding (LPC), have the advantages of good quantization accuracy and low spectral sensitivity. However, computing the LSPs frequencies takes a long time. To address this issue, a fast computation algorithm, based on the Bairstow method for computing LSPs frequencies from linear prediction coefficients, is proposed in this paper. The algorithm process first transforms the symmetric and antisymmetric polynomial to general polynomial, then extracts the polynomial roots. Associated with the short-term stationary property of speech signal, an adaptive initial method is applied to reduce the average iteration numbers by 26%, as compared to the statics in the initial method, with a Perceptual Evaluation of Speech Quality (PESQ) score reaching 3.46. Experimental results show that the proposed method can extract the polynomial roots efficiently and accurately with significantly reduced computation complexity. Compared to previous works, the proposed method is 17 times faster than Tschirnhus Transform, and has a 22% PESQ improvement on the Birge-Vieta method with an almost comparable computation time.