Folding frequency: Difference between revisions

Latest revision as of 14:15, 20 February 2012

folding frequency

(Also called Nyquist frequency.) The highest frequency that can be measured using discretely sampled data.

It is given by n_f (rad s^-1) = π/Δt, where n_f is the Nyquist frequency and t is the time increment between observations. Stated another way, a minimum of two data points is needed to define a wave, hence the period of the smallest wave (i.e., the period corresponding to the Nyquist frequency) that can be measured is 2Δt. The word "folding" comes about because any frequencies that are higher than the Nyquist frequency in a continuous signal will be aliased or folded into lower frequencies when the signal is discretely sampled. To avoid this severe problem, the original signal must be filtered by analog or physical methods to remove all frequencies higher than the Nyquist frequency before the signal is sampled or digitized.

INDEX
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
V
W
X
Y
Z
0
1
2
3
4
5
6
7
8
9

@@ Line 9: / Line 9: @@
    </div>
-<div class="definition"><div class="short_definition">(<br/>''Also called'' Nyquist frequency.) The highest [[frequency]] that can be measured  using discretely sampled data.</div><br/> <div class="paragraph">It is given by ''n''<sub>''f''</sub> (rad s<sup>&minus;1</sup>) = &#x003c0;/&#x00394;''t'', where ''n''<sub>''f''</sub> is the Nyquist frequency and ''t'' is the time increment  between observations. Stated another way, a minimum of two data points is needed to define a  [[wave]], hence the [[period]] of the smallest wave (i.e., the period corresponding to the Nyquist frequency)  that can be measured is 2&#x00394;''t''. The word &ldquo;folding&rdquo; comes about because any frequencies  that are higher than the Nyquist frequency in a continuous [[signal]] will be aliased or folded into  lower frequencies when the signal is discretely sampled. To avoid this severe problem, the original  signal must be filtered by [[analog]] or physical methods to remove all frequencies higher than the  Nyquist frequency before the signal is sampled or digitized.</div><br/> </div>
+<div class="definition"><div class="short_definition">(''Also called'' Nyquist frequency.) The highest [[frequency]] that can be measured  using discretely sampled data.</div><br/> <div class="paragraph">It is given by ''n''<sub>''f''</sub> (rad s<sup>-1</sup>) = &#x003c0;/&#x00394;''t'', where ''n''<sub>''f''</sub> is the Nyquist frequency and ''t'' is the time increment  between observations. Stated another way, a minimum of two data points is needed to define a  [[wave]], hence the [[period]] of the smallest wave (i.e., the period corresponding to the Nyquist frequency)  that can be measured is 2&#x00394;''t''. The word "folding" comes about because any frequencies  that are higher than the Nyquist frequency in a continuous [[signal]] will be aliased or folded into  lower frequencies when the signal is discretely sampled. To avoid this severe problem, the original  signal must be filtered by [[analog]] or physical methods to remove all frequencies higher than the  Nyquist frequency before the signal is sampled or digitized.</div><br/> </div>
 </div>