Signal Processing and Linear Systems-B.P.Lathi copy

# Signal Processing and Linear Systems-B.P.Lathi copy

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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 everlasting signals. 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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## This note was uploaded on 04/14/2013 for the course ENG 350 taught by Professor Bayliss during the Spring '13 term at Northwestern.

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