Signals and Systems Signals operationsLecture 3Khosrow GhadiriElectrical Engineering DepartmentElectrical Engineering DepartmentSan Jose State UniversitySignals operationsFor any signal when the argument is changed to for any real ftat bFor any signal when the argument is changed to for any real positive number a and b.Where the signal is contracted by and shifted to the left by fbfat b fata at bftbaaWhere the signal is contracted by and shifted to the left by units with sign and shifted to the right by with sign. AndWhere the signal is reflected and contracted by and shifted to bfatb fata ftbabaftaaWhere the signal is reflected and contracted by and shifted to the left by units with sign and shifted to the right by units with sign. The important signal operation are: Shiftingftaba baShifting Reflecting Time-scaling ©Khosrow Ghadiri Signal and System 2A signalFor the function shown in the figure below find analytic expressions ftFor the function shown in the figure below, find analytic expressions for and plot the following function versus time:0tftft121t 10.5 0 21100Otherwisettyt f t t ©Khosrow Ghadiri Signal and System 3ContractionFor the function shown in the figure below find analytic ftFor the function shown in the figure below, find analytic expressions for and plot versus time: The time-scaling operation. Using the fundamental definition of a function2ft1 0.5 2 0 2 2ttftis contracted by a factor of 2 21 1200Otherwiseyt f t t ftis contracted by a factor of 2.12ftft101tt1t 10121 0.500Otherwisettyt f t t ©Khosrow Ghadiri Signal and System 410.5Expansion For the function shown in the figure below, find analytic 1ftg,yexpressions for and plot the following function versus time:13ftf11,0 66tt111 0.5 0 233tt611, 3 030, otherwiseft t11110330Otherwiseft t widened or expanded by a factor of 3.ftft1 ©Khosrow Ghadiri Signal and System 523t64ShiftingFor the function shown in the figure below find analytic ftFor the function shown in the figure below, find analytic expressions for and plot the following function versus time: The shifting operation. Using the fundamental definition of a function, we obtain:3ftft10.5 3 0 3 231 1 300Otherwisettft t 2.5 0.5 3 531 2 30Otherwisettft t 0Otherwiseft15t ©Khosrow Ghadiri Signal and System 652t3shiftingFor the function shown in the figure below find analytic ftFor the function shown in the figure below, find analytic expressions for and plot the following function versus time:4ftft10.5 4 241 5 4ttft t 10.5 4 0 4 21140ttft t shifted 4 units to the left.ft41 5 40otherwiseft t 11400Otherwiseft tft12t4 ©Khosrow Ghadiri Signal and System 725t4ReflectionFor the function shown in the figure below find analytic ftFor the function shown in the figure below, find analytic expressions for and plot the following function versus time: The Reflecting Operation. Using the fundamental definition of a function, we obtain:ftft10.5 2 01010otherwisettftt10.5 0 21100otherwisettft t is reflected about the vertical axis.ftft1t ©Khosrow Ghadiri Signal and System 811t2Reflection and expansionFor the function f(t) shown in the figure below find analytic expressions For the function f(t) shown in the figure below, find analytic expressions for and plot the following function versus time:12ft1110.5 0 222tt 10.25 4 01tt11110220Otherwiseft t 110220Otherwiseft t Reflected and then widened by 2 units or vice versa.ftft1t ©Khosrow Ghadiri Signal and System 911t2342Reflection and shiftFor the function shown in the figure below find analytic expressions ftFor the function shown in the figure below, find analytic expressions for and plot the following function versus time:3ft10.53 0 3 231 130ttft t ft0.5 0.5 1 331 34ttft t is reflected and then shifted by 3 units to the right.31 1300otherwiseft t3ftft31 340 otherwiseft t13ft12t34 ©Khosrow Ghadiri Signal and System 101234Contraction and shiftingFor the function shown in the figure below find analytic expressions ftFor the function shown in the figure below, find analytic expressions for and plot the following function versus time:23ft111.52 3 25 15 25tfftWherecontracted by a factor of 2 and then shifted 1.5 units to the 23 2.51.52.50, otherwisefttt ftWherecontracted by a factor of 2 and then shifted 1.5 units to the right. 23ftft1151t25 ©Khosrow Ghadiri Signal and System 111.512.5Reflection, contraction and shiftingFor the function f(t) shown in the figure below find analytic expressions For the function f(t) shown in the figure below, find analytic expressions for and plot the following function
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