Reconstructing a Sampled Signal Using Interpolation

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.