1 PROBLEM 001 PROBLEM 1: Write analytical expression for the continuous-time waveform()ft , shown in below figure. ()ftt3−1−5732 SOLUTION 001 Write analytical expression for the continuous-time waveform()ft , shown in below figure. ()ftt3−1−573 SOLUTION 1: ()()11 1 2 2 13, 0 1, 3Px y Px y==− = ==− = () ()()()30 30(3)331(3) 2ft t t ut−−= −− = + +−−− t3−1− 53t3−1−3 ()()3112tut−++ ()()3552tut−−− ()()3772tut−− () ()()()()()()()()333333 11 55 772222ft tut tut tut tut= + +− + +− − −+ − −3 PROBLEM 002 PROBLEM 2: Write analytical expression for the continuous-time waveform()ft , shown in below figure. ()ftt2− 423 Write analytical expression for the continuous-time waveform()ft , shown in below figure.4 SOLUTION 002 ()ftt2− 432 SOLUTION 2: ()22ut+ ()()23 3tut−−− ()()24 4tut+−− () ( )()()()()2223 324 4f t ut t ut t ut=+−− −+− −5 PROBLEM 003 PROBLEM 3: Write analytical expression for the continuous-time waveform()ft , shown in below figure. ()ftt0456105−5−6 SOLUTION 003 Write analytical expression for the continuous-time waveform()ft , shown in below figure. ()ftt0456105− SOLUTION 3: () () ()()() ()()()()55 15 54 5 4 4 6 6 10 1044 2 2f t tut tut t ut t ut t ut=−−−−−+−−−−−7 PROBLEM 004 PROBLEM 4: Plot the following continuous-time waveform. ()()()()()()()()( )55 111155f t t ut t ut t ut t ut=−+ + ++ ++− −−− −8 SOLUTION 004 Plot the following continuous-time waveform. ()()()()()()()()( )55 111155f t t ut t ut t ut t ut=−+ + ++ ++− −−− − SOLUTION 4: ()()55tut−+ +t005−5−t0()()11tut++1−1t0()()11tut−−1−1()()55tut−−−t5 ()ftt5−1−4−159 PROBLEM 005 PROBLEM 5: Plot the following continuous-time waveform. ()()()()()6335 567ft ut t ut ut=−−− −+−10 SOLUTION 005 Plot the following continuous-time waveform. ()()()()()6335 567ft ut t ut ut=−−− −+− SOLUTION 5: ()63ut−t65t3()()35 3tut−−()67ut−t67 ()ftt676−3511 PROBLEM 006 PROBLEM 6: Write analytical expression for the discrete-time waveform[]fn , shown in below figure. []fnn3−1−573••L••L432102−••12 SOLUTION 006 Write analytical expression for the discrete-time waveform[]fn , shown in below figure. []fnn3−1−573••L••L432102−•• SOLUTION 6: []()[]()[]()[]1122 2 5 5fn n un n un n un=+ +− − −+− −13 PROBLEM 007 PROBLEM 7: Write analytical expression for the discrete-time waveform[]fn , shown in below figure. []fnn3−1−573••L••L432102−14 SOLUTION 007 Write analytical expression for the discrete-time waveform[]fn , shown in below figure. []fnn3−1−573••L••L432102− SOLUTION 7: []()[]()[]()[]()[]22113366f n n un n un n un n un=+ +−− −−− −+− −15 PROBLEM 008 PROBLEM 8: Write analytical expression for the discrete-time waveform[]fn , shown in below figure. []fnn3−1−573••L••L 432102−6•16 SOLUTION 008 Write analytical expression for the discrete-time waveform[]fn , shown in below figure. []fnn3−1−573••L••L 432102−6• SOLUTION 8: [][]()[][]363 336fn un n un un=−−−+−17 PROBLEM 009 PROBLEM 9: Plot the following discrete-time waveform[]fn . []()[][]()[]552 1010fn n un nun n un=+ +− +− −18 SOLUTION 009 Plot the following discrete-time waveform[]fn . []()[][]()[]552 1010fn n un nun n un=+ +− +− − SOLUTION 9: []fnn3−1−575•LL432102−•••4−5−86910111219 PROBLEM 010 PROBLEM 10: Sketch the sequence[]fn . [] [ ] [ ]25fn un an=−−−20 SOLUTION 010 Sketch the sequence[]fn . [] [ ] [ ]25fn un an=−−− SOLUTION 010: []fnt3−1−57•L432102−••4−186•••21 PROBLEM 011 PROBLEM 011: Write analytical expression for the periodic waveform()Pft , shown in below figure. 4−46202−t()pftLL22 SOLUTION 011 Write analytical expression for the periodic waveform()Pft , shown in below figure. 4−46202−t()pftLL SOLUTION 011: ()( )34 24kut k ut k∞=−∞−−−−∑23 PROBLEM 012 PROBLEM 012: Write analytical expression for the periodic waveform()Pft , shown in below figure. 2− 23101−t()pft4LL24 SOLUTION 012 Write analytical expression for the periodic waveform()Pft , shown in below figure. 2− 23101−t()pft4LL SOLUTION 012: () ( ) ( )21Pkftutkutk∞=−∞=−−−−∑ ()( )22 121ut k ut k−−−− −25 PROBLEM 013 PROBLEM 013: Write analytical expression for the periodic waveform()Pft , shown in below figure. 4−45202−t()pft135−1−3−226 SOLUTION 013 Write analytical expression for the periodic waveform()Pft , shown in below figure. 4−45202−t()pft135−1−3−2 SOLUTION 013: () ( ) ( )214