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Unformatted text preview: tants.
2. A n a nalog s ignal is a signal whose amplitude can take on any value over a continuum. O n t he o ther hand, a signal whose amplitudes can take on only a finite
number of values is a digital signal. T he t erms discrete-time and continuoustime qualify t he n ature of a signal along the time axis (horizontal axis). T he
t erms a nalog a nd digital, on t he o ther hand, qualify t he n ature of t he signal
amplitude (vertical axis).
3. A p eriodic s ignal f (t) is defined by t he fact t hat f (t) = f (t + To) for some
To. T he s mallest value of To for which this relationship is satisfied is called t he
p eriod. A periodic signal remains unchanged when shifted by a n integral multiple of its period. A periodic signal can be generated by a periodic extension
of any segment of f (t) of duration To. Finally, a periodic signal, by definition,
must exist over t he e ntire time interval - 00 < t < 0 0. A signal is a periodic i f
i t is n ot p eriodic.
A n e verlasting signal s tarts a t t = - 00 a nd continues forever to t = 0 0. A
c ausal s ignal is a signal t hat is zero for t < O. Hence, periodic signals are
4. A signal w ith finite energy is a n e nergy signal. Similarly a signal with a finite
a nd n onzero power (mean square value) is a p ower signal. A signal can either
be an e nergy signal or a power signal, b ut n ot both. However, there are signals
t hat a re n either energy nor power signals.
5. A signal whose physical description is known completely in a mathematical or
graphical form is a d eterministic signal. A r andom signal is known only in
terms o f i ts p robabilistic description such as mean value, mean square value,
a nd so on, r ather t han its mathematical or graphical form.
A signal f (t) delayed by T seconds (right-shifted) is given b y f (t - T); o n t he
o ther hand, f (t) advanced by T (left-shifted) is given by f (t + T ). A signal f (t)
t ime-compressed by a factor a (a > 1) is given by f (at); on t he o ther hand, t he same 1.9 S ummary 95 signal time-expanded by factor a is given by f(~). T he s ame signal time-inverted
is given by f ( - t).
T he u nit step function u (t) is very useful in representing causal signals and
signals with different mathematical descriptions over different intervals.
In t he classical definition, t he u nit impulse function 8(t) is c haracterized by
u nit area, a nd t he fact t hat i t is c oncentrated a t a single i nstant t = O. T he impulse
function has a sampling (or sifting) property, which s tates t hat t he a rea under t he
p roduct of a function with a u nit impulse is equal t o t he value of t hat function a t
t he i nstant where t he impulse is l ocated (assuming t he function t o b e continuous
a t t he impulse location). In the modern approach, t he impulse function is viewed
as a generalized function a nd is defined by t he sampling property.
T he e xponential function e st, where s is complex, encompasses a large class
of signals t hat includes a constant, a monotonic exponential, a...
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