cartesian2polar.m

Converts the [RF_x, RF_y] representation of a pulse waveform and the derivatives of any function with respect to those RF values into the [RF_amplitude, RF_phase] representation and the derivatives of the function with respect to amplitudes and phases.

Syntax

    [r,p,Dr,Dp,Drr,Drp,Dpr,Dpp]=...
                      cartesian2polar(x,y,Dx,Dy,Dxx,Dxy,Dyx,Dyy)

Parameters

   x    - vector of waveform amplitudes along X

   y    - vector of waveform amplitudes along Y

   Dx   - optional vector of derivatives of a scalar function
          with respect to the waveform amplitudes along X

   Dy   - optional vector of derivatives of a scalar function
          with respect to the waveform amplitudes along Y

   Dxx  - optional matrix of second derivatives of a scalar function
          with respect to the waveform amplitudes along X

   Dxy  - optional matrix of second derivatives of a scalar function
          with respect to the waveform amplitudes along X and Y

   Dyx  - optional matrix of second derivatives of a scalar function
          with respect to the waveform amplitudes along Y and X

   Dyy  - optional matrix of second derivatives of a scalar function
          with respect to the waveform amplitudes along Y

Outputs

   r    - vector of waveform amplitudes

   p    - vector of waveform phases

   Dr   - vector of derivatives of the function with respect
          to the waveform amplitudes.

   Dp   - vector of derivatives of the function with respect
          to the waveform phases.

   Drr  - matrix of second derivatives of the function with respect
          to the waveform amplitudes.

   Drp  - matrix of second derivatives of the function with respect
          to the waveform amplitudes and phases.

   Dpr  - matrix of second derivatives of the function with respect
          to the waveform phases and amplitudes.

   Dpp  - matrix of second derivatives of the function with respect
          to the waveform phases.

See also

polar2cartesian.m, shaped_pulse_xy.m, shaped_pulse_af.m

Version 2.4, authors: David Goodwin, Ilya Kuprov