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 such bins, .
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