<s>
The	O
spectral	B-Algorithm
correlation	I-Algorithm
density	I-Algorithm
(	O
SCD	O
)	O
,	O
sometimes	O
also	O
called	O
the	O
cyclic	O
spectral	O
density	O
or	O
spectral	O
correlation	O
function	O
,	O
is	O
a	O
function	O
that	O
describes	O
the	O
cross-spectral	O
density	O
of	O
all	O
pairs	O
of	O
frequency-shifted	O
versions	O
of	O
a	O
time-series	O
.	O
</s>
<s>
The	O
spectral	B-Algorithm
correlation	I-Algorithm
density	I-Algorithm
applies	O
only	O
to	O
cyclostationary	O
processes	O
because	O
stationary	O
processes	O
do	O
not	O
exhibit	O
spectral	O
correlation	O
.	O
</s>
<s>
The	O
spectral	B-Algorithm
correlation	I-Algorithm
density	I-Algorithm
is	O
closely	O
related	O
to	O
each	O
of	O
the	O
bilinear	O
time-frequency	O
distributions	O
,	O
but	O
is	O
not	O
considered	O
one	O
of	O
Cohen	O
's	O
class	O
of	O
distributions	O
.	O
</s>
<s>
The	O
cyclic	B-Algorithm
auto-correlation	I-Algorithm
function	O
of	O
a	O
time-series	O
is	O
calculated	O
as	O
follows	O
:	O
</s>
<s>
By	O
the	O
Wiener	O
–	O
Khinchin	O
theorem	O
[	O
questionable	O
,	O
discuss ]	O
,	O
the	O
spectral	B-Algorithm
correlation	I-Algorithm
density	I-Algorithm
is	O
then	O
:	O
</s>
<s>
If	O
with	O
MATLAB	B-Language
or	O
the	O
NumPy	B-Application
library	O
in	O
Python	B-Language
,	O
the	O
steps	O
are	O
rather	O
simple	O
to	O
implement	O
.	O
</s>
<s>
Let	O
the	O
signal	O
,	O
or	O
block	O
of	O
IQ	O
samples	O
,	O
be	O
a	O
complex	O
valued	O
tensor	B-Device
,	O
or	O
multidimensional	O
array	O
,	O
of	O
shape	O
,	O
where	O
each	O
element	O
is	O
an	O
IQ	O
sample	O
.	O
</s>
<s>
is	O
a	O
tensor	B-Device
of	O
shape	O
,	O
and	O
depends	O
on	O
how	O
many	O
frames	O
were	O
able	O
to	O
fit	O
in	O
.	O
</s>
<s>
Next	O
a	O
windowing	B-Language
function	I-Language
of	O
shape	O
,	O
like	O
the	O
Hamming	O
window	O
,	O
is	O
applied	O
to	O
each	O
row	O
in	O
.	O
</s>
<s>
Next	O
the	O
FFTs	O
are	O
autocorrelated	O
to	O
create	O
a	O
tensor	B-Device
of	O
shape	O
.	O
</s>
<s>
where	O
H	O
denotes	O
Hermitian	B-Algorithm
(	O
conjugate	O
and	O
transpose	O
)	O
of	O
a	O
matrix	O
.	O
</s>
<s>
is	O
the	O
full	O
SCD	O
,	O
but	O
in	O
the	O
shape	O
of	O
a	O
3-dimensional	O
tensor	B-Device
.	O
</s>
<s>
What	O
we	O
aim	O
for	O
is	O
a	O
2-dimensional	O
tensor	B-Device
(	O
a	O
matrix	O
or	O
image	O
)	O
of	O
shape	O
where	O
each	O
entry	O
corresponds	O
to	O
a	O
particular	O
frequency	O
and	O
cyclic	O
frequency	O
.	O
</s>
<s>
All	O
values	O
of	O
in	O
can	O
be	O
arranged	O
in	O
the	O
tensor	B-Device
,	O
and	O
all	O
values	O
of	O
in	O
in	O
the	O
tensor	B-Device
.	O
</s>
