  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
