F₀ estimation of speech using a complex adaptive pre-emphasis based on the ℓ₂-norm regularized TV-CAR speech analysis

Linear Predictive (LP) analysis has been one of the most successful methods for speech analysis. It is widely used in applications such as smartphone speech coding and communication platforms like TEAMS and Zoom. However, LP analysis does have certain drawbacks, notably lower estimation accuracy due to its least-squares scheme. In response to these limitations, we have introduced an innovative approach called Time-Varying Complex Auto-Regressive (TV-CAR) speech analysis, which is built on Minimum Mean Square Error (MMSE), robustness, and LASSO analysis principles. We evaluated the performance of TV-CAR analysis regarding F<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</inf> estimation in speech and robust speech recognition. Additionally, we proposed ℓ<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</inf>-norm regularized TV-CAR analysis, Regularized LP (RLP)-based analysis, Time-RLP (TRLP)-based analysis, and hybrid methods that combine these approaches. We conducted evaluations focusing on F<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</inf> estimation using the IRAPT method, leveraging complex residuals. Moreover, we previously introduced a Bone-Conducted (BC) prefilter to enhance overall performance. This paper presents an improved F<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</inf> estimation technique that incorporates complex-valued Adaptive Pre-Emphasis (APE), showcasing its effectiveness. Furthermore, we delve into the frame-based computation of analytic signals.