amp_root.m

Amplifier compression distortion model. Applies a saturating root-sigmoidal distortion to the waveform amplitude:

    y=x/(1+(x/a)^s)^(1/s)

Treats odd channels of multi-channel waveform as X and even ones as Y components; the autodiff Jacobian is returned for the vectorisation of the input array.

Syntax

    [w,J]=amp_root(w,sat_lvls,s)

Parameters

   w         - waveform in rad/s nutation frequency units,
               one time slice per column, and rows arran-
               ged as XYXY... with respect to in-phase and
               quadrature parts on each control channel

   sat_lvls  - saturation levels beyond which the amplifi-
               er cannot go, one value per X,Y pair in w,
               giving the maximum output sqrt(X^2+Y^2)

   s         - a vector of positive integers (one value per
               X,Y pair in w) regulating the sharpness of
               the transition from linear to saturating be-
               haviour, a good starting choice is 4

Outputs

   w         - distorted waveform in the same units and 
               layout as the input

   J         - distortion Jacobian matrix with respect to
               the vectorisation of the input, sparse

See also

amp_tanh.m, firf.m, kernelest.m, no_dist.m, penalty.m, restrans.m, spf.m, szf.m, transfermat.m, Optimal_control_module

Version 2.11, authors: Uluk Rasulov, Ilya Kuprov