Differentiable Adaptive Short-Time Fourier Transform with Respect to the Window Length
Maxime Leiber, Yosra Marnissi, Axel Barrau, Mohamed El Badaoui
Abstract
This paper presents a gradient-based method for on-the-fly optimization for both per-frame and per-frequency window length of the short-time Fourier transform (STFT), related to previous work in which we developed a differentiable version of STFT by making the window length a continuous parameter. The resulting differentiable adaptive STFT possesses commendable properties, such as the ability to adapt in the same time-frequency representation to both transient and stationary components, while being easily optimized by gradient descent. We validate the performance of our method in vibration analysis.
Topics & Concepts
Short-time Fourier transformDifferentiable functionFourier transformGradient descentWindow functionWindow (computing)Computer scienceTime–frequency representationTime–frequency analysisAlgorithmMathematicsFrame (networking)Transient (computer programming)Discrete-time Fourier transformArtificial intelligenceFourier analysisMathematical analysisComputer visionArtificial neural networkOperating systemFilter (signal processing)TelecommunicationsStructural Health Monitoring TechniquesAdvanced Adaptive Filtering TechniquesPower Quality and Harmonics