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Signal Reconstruction – the Cardinal Series
Author: John M. Cimbala, Penn State University
Latest revision: 13 February, 2006, 5:30 p.m.
Introduction
•
In a previous learning module, we discuss how to convert an analog signal into a digital signal.
•
In this learning module, we discuss how to
reconstruct
a digital signal back into an analog signal.
Signal Reconstruction
•
As long as the Nyquist criterion is met (sampling frequency
f
s
is at least twice the maximum signal
frequency), we can theoretically reconstruct the original analog waveform from a set of discrete samples.
•
One method of reconstruction is the
cardinal series
. It is the only reconstruction technique we discuss here.
•
For
N
discrete data points, the cardinal series is
()
1
0
sin
1
nN
d
n
t
n
t
ft
f nt
t
n
t
π
=−
=
⎡
⎤
⎛⎞
−
⎜⎟
⎢
⎥
Δ
⎝⎠
⎣
⎦
=Δ
−
Δ
∑
, where
t
is time (we
assume that the signal starts at
t
= 0),
n
is the data point number (the summation is over all
N
discrete data
points, from
n
= 0 to
n
=
N
– 1),
f
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