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Reconstructing a Sampled Signal Using Interpolation

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continuous signal
cos(440πt)
0.3sin(176πt)+cos(88πt)-0.15cos(352πt)
sampling points
3
interpolation method
band-limited
If a continuous signal
f(t)
is sampled with a sampling period
T
then how can you approximately reconstruct the original signal? Three methods that are in use are zero-order hold interpolation, first-order hold interpolation, and band-limited interpolation. The reconstructed signal is calculated using
N-1
∑
n=0
f(nT)h(t-nT)
, where
f(nT)
is the value of the sample taken at time
nT
and
h
is one of the three interpolation functions.
The first plot shows one of two choices for a continuous signal
f(t)
. The points on the second plot are the samples
f(nT)
for
n=0,1,…,N-1
, where
N
is controlled by the slider labeled "sampling points". The third plot shows the sample points along with the last term of the sum. The fourth plot shows all
N
terms of the sum, while the fifth plot adds those terms together. The last plot shows the reconstructed signal in blue together with the original signal in magenta.
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