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Sampling and Reconstruction of Analog Signals 91
(a)
F, Hz
Ideal D/A converter response
(b)
Aliased component
Aliased component
F, Hz
(c)
FIGURE 3.15
Fourier transforms of the sinusoidal signals x a(t), x(n), and y a(t)
which is a rectangular pulse. The resulting signal is a piecewise-constant
(staircase) waveform which requires an appropriately designed analog
postfilter for accurate waveform reconstruction.
x(n) −→ ZOH −→ ˆx a (t) −→ Postfilter −→ x a (t)
• 1st-order-hold (FOH) interpolation: In this case the adjacent samples
are joined by straight lines. This can be obtained by filtering the
impulse train through
⎧
1+ t , 0 ≤ t ≤ T s
⎪⎨ T s
h 1 (t) =
1 − t , T s ≤ t ≤ 2T s
T s
⎪⎩
0, otherwise
Once again, an appropriately designed analog postfilter is required
for accurate reconstruction. These interpolations can be extended
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