Exact FFT-based identification of autoregressive (AR) model
Shigeru Ando · The Journal of the Acoustical Society of America · 2019
In this study, we extend the weighted integral method (WIM) based on differential equation modeling and finite duration observation [IEEE Trans. SP 57, 9 (2009); Inverse Problems 26, 015011 (2010); and JASA 134(4) (2013)] to a discrete WIM with difference equation (DE) modeling and finite length sampled data sequence, and obtain a novel theory and algorithm for short-time signal analysis and spectral estimation.The discrete WIM is composed of three steps: (1) provide the DE (AR model) with unknown coefficients which is satisfied in finite observation interval. (2) Weighted sum the DE with orthogonal sequences (FFT) to obtain algebraic equations (AEs) among the weighted sums in the interval (discrete Fourier coefficients). A mathematical technique is introduced to maintain circulantness of the time shifts. (3) Solve simultaneously a sufficient number of AEs with least squares criterion to obtain the unknowns exactly when the driving term is absent, or to obtain the ones minimizing the driving power when it is present.This approach will be important both in theoretical aspects and in practical usage for resolution-enhanced time-frequency analysis in multi-harmonics and multi-resonance mixture conditions. We compare the performance with other methods and CRLB, and show several experiments using speech and music signals.