# polar2cartesian.m

From Spinach Documentation Wiki

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

## Syntax

[x,y,Dx,Dy,Dxx,Dxy,Dyx,Dyy]=polar2cartesian(r,p,Dr,Dp,Drr,Drp,Dpr,Dpp)

## Arguments

r - vector of waveform amplitudes p - vector of waveform phases Dr - optional vector of derivatives of some scalar function with respect to the waveform amplitudes. Dp - optional vector of derivatives of some scalar 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.

## Outputs

x - vector of waveform amplitudes along X y - vector of waveform amplitudes along Y Dx - vector of derivatives of the function with respect to the waveform amplitudes along X Dy - vector of derivatives of the 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

## See also

cartesian2polar.m, shaped_pulse_xy.m, shaped_pulse_af.m

*Version 2.4, authors: David Goodwin, Ilya Kuprov*