PPT: Sampling & Reconstruction | Signals and Systems - Electrical Engineering (EE) PDF Download

 Page 1


1
Sampling & Reconstruction
Page 2


1
Sampling & Reconstruction
23 Nov'09 Comp30291 Sectn 6 2
 This section concerns the sampling & digitisation of
analogue signals.
 The signals may then be processed digitally and/or
transmitted in digital form.
 Resulting digital signals often need to be converted back to
analogue form or “reconstructed”.
 Reconstruction is also considered in this section.
Introduction
Page 3


1
Sampling & Reconstruction
23 Nov'09 Comp30291 Sectn 6 2
 This section concerns the sampling & digitisation of
analogue signals.
 The signals may then be processed digitally and/or
transmitted in digital form.
 Resulting digital signals often need to be converted back to
analogue form or “reconstructed”.
 Reconstruction is also considered in this section.
Introduction
3
An analogue signal & its magnitude spectrum.
t
x
a
(t)
w
|X
a
(jw)|
Page 4


1
Sampling & Reconstruction
23 Nov'09 Comp30291 Sectn 6 2
 This section concerns the sampling & digitisation of
analogue signals.
 The signals may then be processed digitally and/or
transmitted in digital form.
 Resulting digital signals often need to be converted back to
analogue form or “reconstructed”.
 Reconstruction is also considered in this section.
Introduction
3
An analogue signal & its magnitude spectrum.
t
x
a
(t)
w
|X
a
(jw)|
4
Sampling an analogue signal
Measure x
a
(t) at intervals T  to obtain {x[n]}:
{ ..., x[-1], x[0], x[1], x[2], x[3], ... }
t
x
a
(t)
T       2T     3T     4T     5T -T
-3T   -2T
x[1]
x[2]
x[-1]
x[-2]
x[5]
X[0]
x[3]
x[-3]
x[1] = x
a
(T),      x[2] = x
a
(2T),      etc.
Page 5


1
Sampling & Reconstruction
23 Nov'09 Comp30291 Sectn 6 2
 This section concerns the sampling & digitisation of
analogue signals.
 The signals may then be processed digitally and/or
transmitted in digital form.
 Resulting digital signals often need to be converted back to
analogue form or “reconstructed”.
 Reconstruction is also considered in this section.
Introduction
3
An analogue signal & its magnitude spectrum.
t
x
a
(t)
w
|X
a
(jw)|
4
Sampling an analogue signal
Measure x
a
(t) at intervals T  to obtain {x[n]}:
{ ..., x[-1], x[0], x[1], x[2], x[3], ... }
t
x
a
(t)
T       2T     3T     4T     5T -T
-3T   -2T
x[1]
x[2]
x[-1]
x[-2]
x[5]
X[0]
x[3]
x[-3]
x[1] = x
a
(T),      x[2] = x
a
(2T),      etc.
5
x
S
(t)
t
T         2T       3T       4T       5T
-T
-3T   -2T
x
a
(T
)
x
a
(2T)
x
a
(-T)
x
a
(-2T)
x
a
(4T)
Measure x
a
(t) at 0, ±T, ±2T, ... & represent by analogue impulses.
Invent a new signal x
S
(t) = sample
T
{x
a
(t)}