<s>
The	O
Fourier	B-Algorithm
operator	I-Algorithm
is	O
the	O
kernel	B-Algorithm
of	O
the	O
Fredholm	O
integral	O
of	O
the	O
first	O
kind	O
that	O
defines	O
the	O
continuous	B-Algorithm
Fourier	I-Algorithm
transform	I-Algorithm
,	O
and	O
is	O
a	O
two-dimensional	O
function	O
when	O
it	O
corresponds	O
to	O
the	O
Fourier	B-Algorithm
transform	I-Algorithm
of	O
one-dimensional	O
functions	O
.	O
</s>
<s>
the	O
Fourier	B-Algorithm
transform	I-Algorithm
of	O
a	O
function	O
would	O
be	O
written	O
using	O
the	O
operator	O
as	O
.	O
</s>
<s>
It	O
may	O
be	O
thought	O
of	O
as	O
a	O
limiting	O
case	O
for	O
when	O
the	O
size	O
of	O
the	O
discrete	B-Algorithm
Fourier	I-Algorithm
transform	I-Algorithm
increases	O
without	O
bound	O
while	O
its	O
spatial	O
resolution	O
also	O
increases	O
without	O
bound	O
,	O
so	O
as	O
to	O
become	O
both	O
continuous	O
and	O
not	O
necessarily	O
periodic	O
.	O
</s>
<s>
The	O
Fourier	B-Algorithm
operator	I-Algorithm
defines	O
a	O
continuous	O
two-dimensional	O
function	O
that	O
extends	O
along	O
time	O
and	O
frequency	O
axes	O
,	O
outwards	O
to	O
infinity	O
in	O
all	O
four	O
directions	O
.	O
</s>
<s>
A	O
portion	O
of	O
the	O
infinite	O
Fourier	B-Algorithm
operator	I-Algorithm
is	O
shown	O
in	O
the	O
illustration	O
below	O
.	O
</s>
<s>
Any	O
slice	O
parallel	O
to	O
either	O
of	O
the	O
axes	O
,	O
through	O
the	O
Fourier	B-Algorithm
operator	I-Algorithm
,	O
is	O
a	O
complex	O
exponential	O
,	O
i.e.	O
</s>
<s>
Diagonal	O
slices	O
through	O
the	O
Fourier	B-Algorithm
operator	I-Algorithm
give	O
rise	O
to	O
chirps	O
.	O
</s>
<s>
Thus	O
rotation	O
of	O
the	O
Fourier	B-Algorithm
operator	I-Algorithm
gives	O
rise	O
to	O
the	O
fractional	O
Fourier	B-Algorithm
transform	I-Algorithm
,	O
which	O
is	O
related	O
to	O
the	O
chirplet	B-Algorithm
transform	I-Algorithm
.	O
</s>
