In this paper, we propose a new method for the accurate estimation and tracking of formants in speech signals using time-varying quasi-closed-phase (TVQCP) analysis. Conventional formant tracking methods typically adopt a two-stage estimate-and-track strategy wherein an initial set of formant candidates are estimated using short-time analysis (e.g., 10--50 ms), followed by a tracking stage based on dynamic programming or a linear state-space model. One of the main disadvantages of these approaches is that the tracking stage, however good it may be, cannot improve upon the formant estimation accuracy of the first stage. The proposed TVQCP method provides a single-stage formant tracking that combines the estimation and tracking stages into one. TVQCP analysis combines three approaches to improve formant estimation and tracking: (1) it uses temporally weighted quasi-closed-phase analysis to derive closed-phase estimates of the vocal tract with reduced interference from the excitation source, (2) it increases the residual sparsity by using the $L_1$ optimization and (3) it uses time-varying linear prediction analysis over long time windows (e.g., 100--200 ms) to impose a continuity constraint on the vocal tract model and hence on the formant trajectories. Formant tracking experiments with a wide variety of synthetic and natural speech signals show that the proposed TVQCP method performs better than conventional and popular formant tracking tools, such as Wavesurfer and Praat (based on dynamic programming), the KARMA algorithm (based on Kalman filtering), and DeepFormants (based on deep neural networks trained in a supervised manner). Matlab scripts for the proposed method can be found at: https://github.com/njaygowda/ftrack

翻译：本文提出一种利用时变准闭相分析精确估计与跟踪语音信号共振峰的新方法。传统共振峰跟踪方法通常采用两阶段"估计-跟踪"策略：首先通过短时分析（如10-50毫秒）估计初始共振峰候选集合，随后基于动态规划或线性状态空间模型进行跟踪。这类方法的主要缺陷在于：无论跟踪阶段性能多优，均无法提升第一阶段共振峰估计的精度。所提出的时变准闭相方法将估计与跟踪阶段统一为单阶段共振峰跟踪。时变准闭相分析融合三种策略提升共振峰估计与跟踪性能：(1)采用时域加权准闭相分析，通过降低激励源干扰获取声道闭相估计值；(2)利用$L_1$优化增强残差稀疏性；(3)在长时窗（如100-200毫秒）内使用时变线性预测分析，对声道模型施加连续性约束，进而约束共振峰轨迹。针对多样化的合成语音与自然语音信号进行的共振峰跟踪实验表明，所提时变准闭相方法性能优于传统主流共振峰跟踪工具，包括基于动态规划的Wavesurfer和Praat、基于卡尔曼滤波的KARMA算法，以及基于有监督深度神经网络训练的DeepFormants。本文方法的Matlab脚本可于https://github.com/njaygowda/ftrack 获取。