When estimating the AR and tonal components jointly, there needs to be an initialization step where we get an approximate AR model and an approximate estimate of the tonal parameters. The best way to do this is to first estimate the tonal components with a standard narrow-band detection approach. This uses a median filter in the frequency domain to obtain an estimate of the spectral envelope, which is the smooth spectral shape in the absence of tonals. By dividing the raw spectum by this tonal-free spectral estimate, an esimate of the tonal SNR is obtained at each frequency. Tonals can then be detected by finding bins with SNR above a threshold.

Assume there are $ k$ such bins, $ k\leq L$. A three-point parabolic interpolation can be used to deterine the frequencies more accurately than the DFT bin spacing. At the same time, the AR parameters can be estimated by converting the tonal-free spectrum (from the median filter) to autocorrelation (using inverse DFT), then using the Levinson algorithm to obtain an initial estimate of the AR parameters.

Baggenstoss 2017-05-19