# Dictionary:Analytic signal

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(an ∂l’ ∂d ik)

1. For a signal such as f(t), see Hilbert transform.

2. The analytic signal A of a potential field F is

${\displaystyle {\textbf {A}}(x,y)={\frac {dF}{dx}}{\textbf {i}}+{\frac {dF}{dy}}{\textbf {j}}+{\sqrt {-1}}{\frac {dF}{dz}}{\textbf {k}}}$,

where i, j, k are unit vectors in the x, y, z directions. The analytic signal amplitude (also called the envelope) is

${\displaystyle \left|A\right|={\sqrt {\left({\frac {dF}{dx}}\right)^{2}+\left({\frac {dF}{dy}}\right)^{2}+\left({\frac {dF}{dz}}\right)^{2}}}}$.

If |A| is derived from a magnetic field, it peaks over contacts and its half-width at half maximum (measured perpendicular to strike) equals the depth of the contact. See also analytic signal method.

3. For the definition of analytic, in this sense, see Analytic function.