Bayesian fast Fourier transform approach

The Bayesian fast Fourier transform approach uses the statistical properties of discrete Fourier transforms, instead of the spectral density estimators, to construct the likelihood function and the updated PDF of the model parameters [292]. It does not rely on the approximation of the Wishart distributed spectrum. Expressions of the covariance matrix of the real and imaginary parts of the discrete Fourier transform were given. The only approximation was made on the independency of the discrete Fourier transforms at different frequencies. Therefore, the Bayesian fast Fourier transform approach is more accurate than the spectral density approach in the sense that one of the two approximations in the latter is released. However, since the fast Fourier transform approach considers the real and imaginary parts of the discrete Fourier transform, the corresponding covariance matrices are 2No x 2Nq, instead of No x No in the spectral density approach. Therefore, the spectral density approach is computationally more efficient than the fast Fourier transform approach. 

Yuen, K.-V. and Katafygiotis, L. S. Bayesian fast Fourier transform approach for modal updating using ambient data. Advances in Structural Engineering — An International Journal 6(2) (2003), 81-95. 

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