Digital Signal Processing Reference
In-Depth Information
Z
T
dt\
1:
1
T
x
ð
t
Þ
2
P
¼
lim
T
!1
ð
1
:
1
Þ
T
T
!1
R
T
T
j
x
ð
t
Þj
2
dt should be infinite for power signals.An
energy signal is a signal with finite energy over the time interval (-?, ?), i.e.,
Hence, the energy E
¼
lim
Z
T
dt\
1:
x
ð
t
Þ
2
E
¼
lim
T
!1
ð
1
:
2
Þ
T
It necessarily follows that P = 0 for energy signals. An example of a power signal
is x(t) = sin(x
o
t), and the power of this signal is P = 0.5 W. For this same signal
E = ?. An example of an energy signal is x(t) = e
-|t|
. For this signal E = 1 J and
P = 0.
7. Mono-component and multi-component signals: if only one (possibly time-
varying) frequency component is present in a signal then that signal is said to be
mono-component. If more than one component is present then the signal is
referred to as multi-component. For example, the signal x(t) = sin(x
o
t) ?
cos(5x
o
t) is a 2-component signal; its spectrum (Fourier transform magnitude)
is shown in Fig.
1.4
for f
o
= 1 Hz. The two components are represented by
spikes at the relevant frequencies.
1.1.5 Analog and Digital Signal Processing
Most signals in nature are analog. To process those signals using digital systems,
analog-to-digital (A/D) conversion is first required. Once the analog signal has
been digitized it is typically processed by a digital signal processing (DSP) unit.
Subsequent to that, digital-to-analog (D/A) conversion is applied to recover the
(a)
(b)
(c)
Analog
Discrete−time
Digital
Fig. 1.3
A sinusoid in different versions: a analog, b discrete-time, and c digital version
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