<s>
A	O
sampler	B-Algorithm
is	O
a	O
subsystem	O
or	O
operation	O
that	O
extracts	O
samples	O
from	O
a	O
continuous	O
signal	O
.	O
</s>
<s>
A	O
theoretical	O
ideal	O
sampler	B-Algorithm
produces	O
samples	O
equivalent	O
to	O
the	O
instantaneous	O
value	O
of	O
the	O
continuous	O
signal	O
at	O
the	O
desired	O
points	O
.	O
</s>
<s>
The	O
original	O
signal	O
can	O
be	O
reconstructed	O
from	O
a	O
sequence	O
of	O
samples	O
,	O
up	O
to	O
the	O
Nyquist	O
limit	O
,	O
by	O
passing	O
the	O
sequence	O
of	O
samples	O
through	O
a	O
type	O
of	O
low-pass	B-Algorithm
filter	I-Algorithm
called	O
a	O
reconstruction	O
filter	O
.	O
</s>
<s>
For	O
functions	O
that	O
vary	O
with	O
time	O
,	O
let	O
S(t )	O
be	O
a	O
continuous	O
function	O
(	O
or	O
"	O
signal	O
"	O
)	O
to	O
be	O
sampled	O
,	O
and	O
let	O
sampling	O
be	O
performed	O
by	O
measuring	O
the	O
value	O
of	O
the	O
continuous	O
function	O
every	O
T	O
seconds	O
,	O
which	O
is	O
called	O
the	O
sampling	O
interval	O
or	O
sampling	B-Algorithm
period	I-Algorithm
.	O
</s>
<s>
The	O
sampling	B-Algorithm
frequency	I-Algorithm
or	O
sampling	O
rate	O
,	O
fs	O
,	O
is	O
the	O
average	O
number	O
of	O
samples	O
obtained	O
in	O
one	O
second	O
,	O
thus	O
,	O
with	O
the	O
unit	O
samples	O
per	O
second	O
,	O
sometimes	O
referred	O
to	O
as	O
hertz	O
,	O
for	O
example	O
e.g.	O
</s>
<s>
The	O
Whittaker	O
–	O
Shannon	O
interpolation	O
formula	O
is	O
mathematically	O
equivalent	O
to	O
an	O
ideal	O
low-pass	B-Algorithm
filter	I-Algorithm
whose	O
input	O
is	O
a	O
sequence	O
of	O
Dirac	O
delta	O
functions	O
that	O
are	O
modulated	O
(	O
multiplied	O
)	O
by	O
the	O
sample	O
values	O
.	O
</s>
<s>
That	O
fidelity	O
is	O
reduced	O
when	O
s(t )	O
contains	O
frequency	O
components	O
whose	O
cycle	O
length	O
(	O
period	O
)	O
is	O
less	O
than	O
2	O
sample	B-Algorithm
intervals	I-Algorithm
(	O
see	O
Aliasing	B-Error_Name
)	O
.	O
</s>
<s>
The	O
corresponding	O
frequency	O
limit	O
,	O
in	O
cycles/sec	O
(	O
hertz	O
)	O
,	O
is	O
0.5	O
cycle/sample	O
×	O
fssamples/sec	O
=	O
fs/2	O
,	O
known	O
as	O
the	O
Nyquist	O
frequency	O
of	O
the	O
sampler	B-Algorithm
.	O
</s>
<s>
Therefore	O
,	O
s(t )	O
is	O
usually	O
the	O
output	O
of	O
a	O
low-pass	B-Algorithm
filter	I-Algorithm
,	O
functionally	O
known	O
as	O
an	O
anti-aliasing	O
filter	O
.	O
</s>
<s>
Without	O
an	O
anti-aliasing	O
filter	O
,	O
frequencies	O
higher	O
than	O
the	O
Nyquist	O
frequency	O
will	O
influence	O
the	O
samples	O
in	O
a	O
way	O
that	O
is	O
misinterpreted	O
by	O
the	O
interpolation	O
process	O
.	O
</s>
<s>
Aliasing	B-Error_Name
.	O
</s>
<s>
Some	O
amount	O
of	O
aliasing	B-Error_Name
is	O
inevitable	O
because	O
only	O
theoretical	O
,	O
infinitely	O
long	O
,	O
functions	O
can	O
have	O
no	O
frequency	O
content	O
above	O
the	O
Nyquist	O
frequency	O
.	O
</s>
<s>
Aliasing	B-Error_Name
can	O
be	O
made	O
arbitrarily	O
small	O
by	O
using	O
a	O
sufficiently	O
large	O
order	O
of	O
the	O
anti-aliasing	O
filter	O
.	O
</s>
<s>
Quantization	B-Algorithm
as	O
a	O
consequence	O
of	O
the	O
finite	O
precision	O
of	O
words	O
that	O
represent	O
the	O
converted	O
values	O
.	O
</s>
<s>
Error	O
due	O
to	O
other	O
non-linear	O
effects	O
of	O
the	O
mapping	O
of	O
input	O
voltage	O
to	O
converted	O
output	O
value	O
(	O
in	O
addition	O
to	O
the	O
effects	O
of	O
quantization	B-Algorithm
)	O
.	O
</s>
<s>
Although	O
the	O
use	O
of	O
oversampling	O
can	O
completely	O
eliminate	O
aperture	O
error	O
and	O
aliasing	B-Error_Name
by	O
shifting	O
them	O
out	O
of	O
the	O
passband	O
,	O
this	O
technique	O
cannot	O
be	O
practically	O
used	O
above	O
a	O
few	O
GHz	O
,	O
and	O
may	O
be	O
prohibitively	O
expensive	O
at	O
much	O
lower	O
frequencies	O
.	O
</s>
<s>
Furthermore	O
,	O
while	O
oversampling	O
can	O
reduce	O
quantization	B-Algorithm
error	O
and	O
non-linearity	O
,	O
it	O
cannot	O
eliminate	O
these	O
entirely	O
.	O
</s>
<s>
Consequently	O
,	O
practical	O
ADCs	O
at	O
audio	O
frequencies	O
typically	O
do	O
not	O
exhibit	O
aliasing	B-Error_Name
,	O
aperture	O
error	O
,	O
and	O
are	O
not	O
limited	O
by	O
quantization	B-Algorithm
error	O
.	O
</s>
<s>
At	O
RF	O
and	O
microwave	O
frequencies	O
where	O
oversampling	O
is	O
impractical	O
and	O
filters	O
are	O
expensive	O
,	O
aperture	O
error	O
,	O
quantization	B-Algorithm
error	O
and	O
aliasing	B-Error_Name
can	O
be	O
significant	O
limitations	O
.	O
</s>
<s>
Jitter	O
,	O
noise	O
,	O
and	O
quantization	B-Algorithm
are	O
often	O
analyzed	O
by	O
modeling	O
them	O
as	O
random	O
errors	O
added	O
to	O
the	O
sample	O
values	O
.	O
</s>
<s>
Integration	O
and	O
zero-order	O
hold	O
effects	O
can	O
be	O
analyzed	O
as	O
a	O
form	O
of	O
low-pass	B-Algorithm
filtering	I-Algorithm
.	O
</s>
<s>
Digital	O
audio	O
uses	O
pulse-code	B-Algorithm
modulation	I-Algorithm
(	O
PCM	B-Algorithm
)	O
and	O
digital	O
signals	O
for	O
sound	O
reproduction	O
.	O
</s>
<s>
There	O
has	O
been	O
an	O
industry	O
trend	O
towards	O
sampling	O
rates	O
well	O
beyond	O
the	O
basic	O
requirements	O
:	O
such	O
as	O
96kHz	O
and	O
even	O
192kHz	O
Even	O
though	O
ultrasonic	B-Application
frequencies	O
are	O
inaudible	O
to	O
humans	O
,	O
recording	O
and	O
mixing	O
at	O
higher	O
sampling	O
rates	O
is	O
effective	O
in	O
eliminating	O
the	O
distortion	O
that	O
can	O
be	O
caused	O
by	O
foldback	O
aliasing	B-Error_Name
.	O
</s>
<s>
Conversely	O
,	O
ultrasonic	B-Application
sounds	O
may	O
interact	O
with	O
and	O
modulate	O
the	O
audible	O
part	O
of	O
the	O
frequency	O
spectrum	O
(	O
intermodulation	O
distortion	O
)	O
,	O
degrading	O
the	O
fidelity	O
.	O
</s>
<s>
One	O
advantage	O
of	O
higher	O
sampling	O
rates	O
is	O
that	O
they	O
can	O
relax	O
the	O
low-pass	B-Algorithm
filter	I-Algorithm
design	O
requirements	O
for	O
ADCs	O
and	O
DACs	O
,	O
but	O
with	O
modern	O
oversampling	O
sigma-delta	O
converters	O
this	O
advantage	O
is	O
less	O
important	O
.	O
</s>
<s>
The	O
Audio	O
Engineering	O
Society	O
recommends	O
48kHz	O
sampling	O
rate	O
for	O
most	O
applications	O
but	O
gives	O
recognition	O
to	O
44.1kHz	O
for	O
Compact	O
Disc	O
(	O
CD	O
)	O
and	O
other	O
consumer	O
uses	O
,	O
32kHz	O
for	O
transmission-related	O
applications	O
,	O
and	O
96kHz	O
for	O
higher	O
bandwidth	O
or	O
relaxed	O
anti-aliasing	O
filtering	O
.	O
</s>
<s>
Sampling	O
rate	O
Use	O
8,000	O
Hz	O
Telephone	O
and	O
encrypted	O
walkie-talkie	B-Application
,	O
wireless	O
intercom	O
and	O
wireless	B-Device
microphone	I-Device
transmission	O
;	O
adequate	O
for	O
human	O
speech	O
but	O
without	O
sibilance	O
(	O
ess	O
sounds	O
like	O
eff	O
(	O
,	O
)	O
)	O
.	O
</s>
<s>
11,025	O
Hz	O
One	O
quarter	O
the	O
sampling	O
rate	O
of	O
audio	O
CDs	O
;	O
used	O
for	O
lower-quality	O
PCM	B-Algorithm
,	O
MPEG	O
audio	O
and	O
for	O
audio	O
analysis	O
of	O
subwoofer	O
bandpasses	O
.	O
</s>
<s>
Used	O
in	O
most	O
modern	O
VoIP	B-Application
and	O
VVoIP	O
communication	O
products	O
.	O
</s>
<s>
22,050	O
Hz	O
One	O
half	O
the	O
sampling	O
rate	O
of	O
audio	O
CDs	O
;	O
used	O
for	O
lower-quality	O
PCM	B-Algorithm
and	O
MPEG	O
audio	O
and	O
for	O
audio	O
analysis	O
of	O
low	O
frequency	O
energy	O
.	O
</s>
<s>
High-quality	O
digital	O
wireless	B-Device
microphones	I-Device
.	O
</s>
<s>
44,100	O
Hz	O
Audio	O
CD	O
,	O
also	O
most	O
commonly	O
used	O
with	O
MPEG-1	B-Algorithm
audio	O
(	O
VCD	O
,	O
SVCD	O
,	O
MP3	B-Application
)	O
.	O
</s>
<s>
Originally	O
chosen	O
by	O
Sony	O
because	O
it	O
could	O
be	O
recorded	O
on	O
modified	O
video	O
equipment	O
running	O
at	O
either	O
25	O
frames	O
per	O
second	O
(	O
PAL	B-Language
)	O
or	O
30	O
frame/s	O
(	O
using	O
an	O
NTSC	O
monochrome	O
video	O
recorder	O
)	O
and	O
cover	O
the	O
20	O
kHz	O
bandwidth	O
thought	O
necessary	O
to	O
match	O
professional	O
analog	O
recording	O
equipment	O
of	O
the	O
time	O
.	O
</s>
<s>
A	O
PCM	B-Algorithm
adaptor	O
would	O
fit	O
digital	B-Algorithm
audio	I-Algorithm
samples	I-Algorithm
into	O
the	O
analog	O
video	O
channel	O
of	O
,	O
for	O
example	O
,	O
PAL	B-Language
video	O
tapes	O
using	O
3	O
samples	O
per	O
line	O
,	O
588	O
lines	O
per	O
frame	O
,	O
25	O
frames	O
per	O
second	O
.	O
</s>
<s>
47,250	O
Hz	O
world	O
's	O
first	O
commercial	O
PCM	B-Algorithm
sound	O
recorder	O
by	O
Nippon	O
Columbia	O
(	O
Denon	O
)	O
48,000	O
Hz	O
The	O
standard	O
audio	O
sampling	O
rate	O
used	O
by	O
professional	O
digital	O
video	O
equipment	O
such	O
as	O
tape	O
recorders	O
,	O
video	O
servers	O
,	O
vision	O
mixers	O
and	O
so	O
on	O
.	O
</s>
<s>
Also	O
used	O
for	O
sound	O
with	O
consumer	O
video	O
formats	O
like	O
DV	O
,	O
digital	B-Application
TV	I-Application
,	O
DVD	O
,	O
and	O
films	O
.	O
</s>
<s>
The	O
professional	O
Serial	B-Protocol
Digital	I-Protocol
Interface	I-Protocol
(	O
SDI	O
)	O
and	O
High-definition	O
Serial	B-Protocol
Digital	I-Protocol
Interface	I-Protocol
(	O
HD-SDI	B-Protocol
)	O
used	O
to	O
connect	O
broadcast	O
television	O
equipment	O
together	O
uses	O
this	O
audio	O
sampling	B-Algorithm
frequency	I-Algorithm
.	O
</s>
<s>
96,000	O
Hz	O
DVD-Audio	O
,	O
some	O
LPCM	B-Algorithm
DVD	O
tracks	O
,	O
BD-ROM	O
(	O
Blu-ray	O
Disc	O
)	O
audio	O
tracks	O
,	O
HD	B-Operating_System
DVD	I-Operating_System
(	O
High-Definition	B-Operating_System
DVD	I-Operating_System
)	O
audio	O
tracks	O
.	O
</s>
<s>
This	O
sampling	B-Algorithm
frequency	I-Algorithm
is	O
twice	O
the	O
48	O
kHz	O
standard	O
commonly	O
used	O
with	O
audio	O
on	O
professional	O
equipment	O
.	O
</s>
<s>
176,400	O
Hz	O
Sampling	O
rate	O
used	O
by	O
HDCD	B-Device
recorders	O
and	O
other	O
professional	O
applications	O
for	O
CD	O
production	O
.	O
</s>
<s>
192,000	O
Hz	O
DVD-Audio	O
,	O
some	O
LPCM	B-Algorithm
DVD	O
tracks	O
,	O
BD-ROM	O
(	O
Blu-ray	O
Disc	O
)	O
audio	O
tracks	O
,	O
and	O
HD	B-Operating_System
DVD	I-Operating_System
(	O
High-Definition	B-Operating_System
DVD	I-Operating_System
)	O
audio	O
tracks	O
,	O
High-Definition	O
audio	O
recording	O
devices	O
and	O
audio	O
editing	O
software	O
.	O
</s>
<s>
This	O
sampling	B-Algorithm
frequency	I-Algorithm
is	O
four	O
times	O
the	O
48	O
kHz	O
standard	O
commonly	O
used	O
with	O
audio	O
on	O
professional	O
video	O
equipment	O
.	O
</s>
<s>
Audio	O
is	O
typically	O
recorded	O
at	O
8-	O
,	O
16-	O
,	O
and	O
24-bit	O
depth	O
,	O
which	O
yield	O
a	O
theoretical	O
maximum	O
signal-to-quantization-noise	O
ratio	O
(	O
SQNR	O
)	O
for	O
a	O
pure	O
sine	O
wave	O
of	O
,	O
approximately	O
,	O
49.93dB	O
,	O
98.09dB	O
and	O
122.17dB	O
.	O
</s>
<s>
CD	O
quality	O
audio	O
uses	O
16-bit	B-Algorithm
samples	I-Algorithm
.	O
</s>
<s>
Thermal	O
noise	O
limits	O
the	O
true	O
number	O
of	O
bits	O
that	O
can	O
be	O
used	O
in	O
quantization	B-Algorithm
.	O
</s>
<s>
However	O
,	O
digital	B-General_Concept
signal	I-General_Concept
processing	I-General_Concept
operations	O
can	O
have	O
very	O
high	O
dynamic	O
range	O
,	O
consequently	O
it	O
is	O
common	O
to	O
perform	O
mixing	O
and	O
mastering	O
operations	O
at	O
32-bit	O
precision	O
and	O
then	O
convert	O
to	O
16	O
-	O
or	O
24-bit	O
for	O
distribution	O
.	O
</s>
<s>
For	O
most	O
phonemes	B-Language
,	O
almost	O
all	O
of	O
the	O
energy	O
is	O
contained	O
in	O
the	O
100Hz	O
–	O
4kHz	O
range	O
,	O
allowing	O
a	O
sampling	O
rate	O
of	O
8kHz	O
.	O
</s>
<s>
This	O
is	O
the	O
sampling	O
rate	O
used	O
by	O
nearly	O
all	O
telephony	O
systems	O
,	O
which	O
use	O
the	O
G.711	B-Algorithm
sampling	O
and	O
quantization	B-Algorithm
specifications	O
.	O
</s>
<s>
Standard-definition	B-Device
television	I-Device
(	O
SDTV	B-Device
)	O
uses	O
either	O
720	O
by	O
480	O
pixels	B-Algorithm
(	O
US	O
NTSC	O
525-line	O
)	O
or	O
720	O
by	O
576	O
pixels	B-Algorithm
(	O
UK	O
PAL	B-Language
625-line	O
)	O
for	O
the	O
visible	O
picture	O
area	O
.	O
</s>
<s>
High-definition	B-Device
television	I-Device
(	O
HDTV	B-Device
)	O
uses	O
720p	O
(	O
progressive	O
)	O
,	O
1080i	O
(	O
interlaced	O
)	O
,	O
and	O
1080p	O
(	O
progressive	O
,	O
also	O
known	O
as	O
Full-HD	O
)	O
.	O
</s>
<s>
In	O
digital	O
video	O
,	O
the	O
temporal	O
sampling	O
rate	O
is	O
defined	O
the	O
frame	O
rate	O
or	O
rather	O
the	O
field	O
rate	O
rather	O
than	O
the	O
notional	O
pixel	B-Algorithm
clock	O
.	O
</s>
<s>
The	O
image	O
sampling	B-Algorithm
frequency	I-Algorithm
is	O
the	O
repetition	O
rate	O
of	O
the	O
sensor	O
integration	O
period	O
.	O
</s>
<s>
Since	O
the	O
integration	O
period	O
may	O
be	O
significantly	O
shorter	O
than	O
the	O
time	O
between	O
repetitions	O
,	O
the	O
sampling	B-Algorithm
frequency	I-Algorithm
can	O
be	O
different	O
from	O
the	O
inverse	O
of	O
the	O
sample	B-Algorithm
time	I-Algorithm
:	O
</s>
<s>
When	O
analog	O
video	O
is	O
converted	O
to	O
digital	O
video	O
,	O
a	O
different	O
sampling	O
process	O
occurs	O
,	O
this	O
time	O
at	O
the	O
pixel	B-Algorithm
frequency	O
,	O
corresponding	O
to	O
a	O
spatial	O
sampling	O
rate	O
along	O
scan	B-Algorithm
lines	I-Algorithm
.	O
</s>
<s>
A	O
common	O
pixel	B-Algorithm
sampling	O
rate	O
is	O
:	O
</s>
<s>
Spatial	O
sampling	O
in	O
the	O
other	O
direction	O
is	O
determined	O
by	O
the	O
spacing	O
of	O
scan	B-Algorithm
lines	I-Algorithm
in	O
the	O
raster	B-Algorithm
.	O
</s>
<s>
Spatial	B-Error_Name
aliasing	I-Error_Name
of	O
high-frequency	O
luma	O
or	O
chroma	O
video	O
components	O
shows	O
up	O
as	O
a	O
moiré	O
pattern	O
.	O
</s>
<s>
The	O
process	O
of	O
volume	O
rendering	O
samples	O
a	O
3D	O
grid	O
of	O
voxels	B-Algorithm
to	O
produce	O
3D	O
renderings	O
of	O
sliced	O
(	O
tomographic	O
)	O
data	O
.	O
</s>
<s>
Volume	O
rendering	O
is	O
common	O
in	O
medical	O
imaging	O
,	O
X-ray	O
computed	O
tomography	O
(	O
CT/CAT	O
)	O
,	O
magnetic	O
resonance	O
imaging	O
(	O
MRI	O
)	O
,	O
positron	B-Application
emission	I-Application
tomography	I-Application
(	O
PET	O
)	O
are	O
some	O
examples	O
.	O
</s>
<s>
When	O
a	O
bandpass	O
signal	O
is	O
sampled	O
slower	O
than	O
its	O
Nyquist	O
rate	O
,	O
the	O
samples	O
are	O
indistinguishable	O
from	O
samples	O
of	O
a	O
low-frequency	O
alias	B-Error_Name
of	O
the	O
high-frequency	O
signal	O
.	O
</s>
<s>
That	O
is	O
often	O
done	O
purposefully	O
in	O
such	O
a	O
way	O
that	O
the	O
lowest-frequency	O
alias	B-Error_Name
satisfies	O
the	O
Nyquist	O
criterion	O
,	O
because	O
the	O
bandpass	O
signal	O
is	O
still	O
uniquely	O
represented	O
and	O
recoverable	O
.	O
</s>
<s>
Such	O
undersampling	B-Algorithm
is	O
also	O
known	O
as	O
bandpass	B-Algorithm
sampling	I-Algorithm
,	O
harmonic	O
sampling	O
,	O
IF	O
sampling	O
,	O
and	O
direct	O
IF	O
to	O
digital	O
conversion	O
.	O
</s>
<s>
When	O
one	O
waveform	O
is	O
the	O
Hilbert	B-Algorithm
transform	I-Algorithm
of	O
the	O
other	O
waveform	O
the	O
complex-valued	O
function	O
,	O
is	O
called	O
an	O
analytic	O
signal	O
,	O
whose	O
Fourier	O
transform	O
is	O
zero	O
for	O
all	O
negative	O
values	O
of	O
frequency	O
.	O
</s>
<s>
For	O
instance	O
,	O
the	O
equivalent	O
baseband	O
waveform	O
can	O
be	O
created	O
without	O
explicitly	O
computing	O
by	O
processing	O
the	O
product	O
sequence	O
through	O
a	O
digital	O
low-pass	B-Algorithm
filter	I-Algorithm
whose	O
cutoff	O
frequency	O
is	O
B/2	O
.	O
</s>
