Signal frequency axis

The signal frequency axis stays constant under this transform. Only its description changes. This can be written as

$\displaystyle \ensuremath{f_\ensuremath{\mathrm{sig}}^{\ensuremath{\mathrm{rest}}}}(\ensuremath{i_{\ensuremath{\mathrm{}}}})$ $\textstyle =$ $\displaystyle \ensuremath{f_\ensuremath{\mathrm{sig,old}}^{\ensuremath{\mathrm{...
...ath{\delta \ensuremath{f_\ensuremath{\mathrm{}}^{\ensuremath{\mathrm{rest}}}}},$(44)
  $\textstyle =$ $\displaystyle \ensuremath{f_\ensuremath{\mathrm{sig,new}}^{\ensuremath{\mathrm{...
...ath{\delta \ensuremath{f_\ensuremath{\mathrm{}}^{\ensuremath{\mathrm{rest}}}}},$(45)
with
  $\displaystyle \ensuremath{\delta \ensuremath{f_\ensuremath{\mathrm{}}^{\ensurem...
...nsuremath{\mathrm{\ensuremath{\mathrm{sys}}}}}^{\ensuremath{\mathrm{meas}}}}}.
$ (46)
It is then easy to deduce that only the reference channel must be changed as
  $\displaystyle \ensuremath{i_{\ensuremath{\mathrm{0,new}}}}
= \ensuremath{i_{\e...
...h{\mathrm{\ensuremath{\mathrm{sys}}}}}^{\ensuremath{\mathrm{meas}}}} \right) }
$ (47)