Explicit local sine-probe parameters

Choose $X_z$ containing the spatial support of $z_{\mathrm{red}}$, and set

For $ϵ\le 1,{ϵ}^2{\Lambda }^2\le 1/2$,

A sufficient normalization condition is

It follows by expanding the denominator as $c_0/ϵ+ϵs_{\psi }(j_{ϵ},p_0)$.

Thus, with

the local theorem has the explicit sufficient allowance

First choose finite $L$ to reduce the packet term, then finite positive $ϵ$ to meet the remaining inequalities. No rate in $L$ is claimed.

Finally the uncertainty inequality gives

The processing test grows as ${ϵ}^{-1}$, and the squeeze magnitude is $2\log (1/ϵ)$. A fixed reference probe would instead have residual variance of order ${ϵ}^{-2}$, suppressing the signal. No effect is divided by its attenuation, and no bounded-energy probe-preparation protocol is supplied.