Madagascar Programming Reference Manual

Simple weight operator (weight.c)

This weight operator is defined by

$$y = L_wx=wx, \qquad\textrm{with}\quad y_t\leftarrow w_tx_t.x = L_w^*y=wy,\qquad\textrm{with}\quad x_t\leftarrow w_ty_t.$$

Note that for complex data the weight $w$ must still be real.

There is also an in-place ( $x\leftarrow L_wx$ ) version of the operator, which multiplies the input data with the square of $w$ i.e.

$$x = L_wx=w^2x,\qquad\textrm{ with}\quad x_t\leftarrow w_t^2x_t.$$