How is RN (Residual Noise) calculated?

RN is calculated in the time window specified for Fmp calculation (Fmp start -> Fmp stop time, from test template).

RN estimation is also used in Fsp/Fmp calculation (see below).

There are 3 known methods to estimate residual noise level:

1. using two buffers (A&B, odd/even, etc.): A-B. Simplest known method. "Quick and dirty", almost free of assumptions, but usually not accurate enough...

2. using ensemble variance (i.e. across all sweeps) in a single point [Don, Elberling - Quality estimation of averaged ABR (Scand Audiol), 1984]. Only applicable to simple averaging!

3. using ensemble variance (i.e. across all sweeps) in all points  [Granzow, 2001]  Adapted for weighted averaging.

The formula for RN estimation is based on the following papers:

• Don, M., Elberling, C., and Waring, M.W. (1984). "Objective detection of Averaged auditory brainstem responses, Scand.Audiol. 13, 219-228.

• Granzow M, Riedel H, Kollmeier B (2001) Single-sweep-based methods to improve the quality of auditory brainstem responses. Part I: optimized linear filtering. Z Audiol 40 (1), 32–44

See also:  Don, Elberling - Evaluating residual background noise in human ABR (JASA) [1994]

1st paper suggested to estimate RN as an ensemble (i.e. across ALL sweeps) variance in a single point (actually it is a part of Fsp calculation - VarSP, see below).
But this formula is only applicable to simple averaging (due to the assumptions taken for granted - that distribution of noise is constant)!

2nd paper adapted the formula for weighted averaging. We call it "RN estimation by ensemble variance in all points".

We use this 3rd approach to RN estimation: directly for all sweeps for simple & Hoke averaging, and for sub-averaged sweeps for Bayesian (since Bayesian first averages small blocks of sweeps using simple averaging).

This approach in our comprehensive testing provided best results for residual noise estimation.

Only for our own weighted averaging algorithm, LSM (least squares method), the results are different: noise estimation by A-B (two buffers, method 1) works best (most accurate estimation), and we use this approach in this case.

That's because our algorithm uses different assumptions about noise: in our case, sub-averages have significantly different residual noises, and the variances of noise are not equal between them.