Page 296 - Electrical Engineering Dictionary

versible power in electromechanical systems. form. Specifically, given the Fourier trans-
For example, in the case of power electronics, form F(f ) = A(f )(u) exp(i 8(f )(u)),
the four-quadrant operation is defined only then A(f ) represents the amplitude. See
with electrical variables to visualize the way Fourier transform.
of energy transfer in a static converter. For
electrical machines, the same operation can Fourier filter a filter, or mask, placed in
be defined with electrical variables at the in- the Fourier transform plane.
put (motor) or at the output (generator) and
also with mechanical variables at the output Fourier binary filter a filter placed in
(motor) or at the input (generator). the Fourier plane of an optical system con-
(2) the four combinations of forward/ structed with only two amplitude or two
reverse rotation and forward/reverse torque phase values.
of which a regenerative drive is capa-
ble. These are: motoring: forward rota- Fourier integral the integral that yields
tion/forward torque; regeneration: forward the Fourier transform of an absolutely inte-
rotation/reverse torque; motor: reverse ro- grable function f over n-dimensional Eu-
tation/reverse torque; and regeneration: re- clidean space:
verse rotation/forward torque. Z
F(f )(u) = f(x) exp[−i u · x] dx
four-wave mixing a nonlinear optical
phenomenon in which four optical beams in-
where the frequency u is expressed in radi-
teract inside nonlinear media or photorefrac-
ans. See also Fourier transform.
tive crystals. When four beams of coherent
electromagnetic radiation intersect inside a Fourier optics optical systems that utilize
nonlinear or photorefractive medium, they the exact Fourier transforming properties of
will, in general, form six interference pat- a lens.
terns and induce six volume refractive index
gratings in the medium. The presence of the Fourier optics relay lens a lens system
index gratings will affect the propagation of that produces the exact Fourier transform of
these four beams. This may lead to energy an image. Two such relay lens will reproduce
coupling. The coupling of the four optical an image without any phase curvature.
beams is referred to as four-wave mixing. In
one of the most useful four-wave mixing con- Fourier phase the phase angle (modulo
figurations, the four beams form two pairs 2π) taken by the Fourier transform. Specif-
of counterpropagating beams. In this par- ically, given the Fourier transform F(f ) =
ticular configuration, some of the refractive A(f )(u) exp(i 8(f )(u)), then 8(f ) repre-
index gratings are identical in their grating sents the phase. See Fourier transform.
wavevectors. This leads to the generation of
phase conjugate waves. Four-wave mixing Fourier phase congruence for a 1-D real-
is a convenient method for the generation of valued signal f and a point p, the Fourier
phase conjugated waves. phase that the signal f would have if the ori-
gin were shifted to p; in other words, it is the
four-way interleaved splitting a resource Fourier phase of f translated by −p. The
into four separate units that may be accessed congruence between the phases at p for the
in parallel for the same request (usually in the various frequencies — in other words the de-
context of memory banks). gree by which those phases at p are close to
each other — can be measured by
Fourier amplitude the amplitude
2
2
angle(modulo2π)takenbytheFouriertrans- f(p) + H(f )(p) ,

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