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36
Signals and Spectra Chap. 2
w(t)
Waveform decays
to zero before
t=
Waveform decays
to zero before
t=
T 2T 3T 4T 5T 6T 7T
t
(a) Physical Waveform
w(t)
Waveform extends
t=
Waveform extends
to t=
T 2T 3T 4T 5T 6T 7T
t
(b) Math Model Waveform
Figure 2–1
Physical and mathematical waveforms.
signals will be given in a subsequent section.) All physical signals are energy signals,
although we generally use power signal mathematical models to simplify the analysis.
In summary, waveforms may often be classified as signals or noise, digital or analog,
deterministic or nondeterministic, physically realizable or nonphysically realizable, and
belonging to the power or energy type. Additional classifications, such as periodic and
nonperiodic, will be given in the next section.
Time Average Operator
Some useful waveform characteristics are the direct “current” (DC) value, average power, and
root-mean-square (RMS) value. Before these concepts are reviewed, the time average operator
needs to be defined.
DEFINITION.
The time average operator † is given by
1
8[# ]9 = lim
T: q T L
T/2
-T/2
[# ] dt
(2–1)
† In Appendix B, the ensemble average operator is defined.