ColorGrayscale Jeffrey Schiano 2014. All rights reserved. Rec 12. EE 350Continuous-Time Linear SystemsRecitation 121 Jeffrey Schiano 2014. All rights reserved. Rec 12. Recitation 12 Topics2• Solved Problems – Fourier Transforms and properties– Application of Fourier Transforms Jeffrey Schiano 2014. All rights reserved. Rec 12. Problem 1• Consider the signal1. Sketch f(t)2. Determine, without computation of the spectra, whether the Fourier transform is an even function of frequency, an odd function of frequency, or neither3. Determine, without computation of the spectra, whether the Fourier transform is purely real, purely imaginary, or a complex-valued function of frequency3( ) rect2tft t Jeffrey Schiano 2014. All rights reserved. Rec 12. Problem 1 Solution4 Jeffrey Schiano 2014. All rights reserved. Rec 12. Problem 1 Solution5 Jeffrey Schiano 2014. All rights reserved. Rec 12. Problem 2• The Fourier transform of a signal f(t) is1. Determine, without computation of f(t), whether the signal f(t) is purely real, purely imaginary, or a complex-valued function of time2. Determine, without computation of f(t), whether the signal f(t) is an even function of time, an odd function of time, or neither64sin() (2 )Fj Jeffrey Schiano 2014. All rights reserved. Rec 12. Problem 2 Solution7 Jeffrey Schiano 2014. All rights reserved. Rec 12. Problem 2 Solution8 Jeffrey Schiano 2014. All rights reserved. Rec 12. Problem 3• A signal f(t) has the Fourier transform1. Determine the energy of the signal f(t) using Parseval’stheorem2. Using an appropriate transform pair and property, determine f(t) 942rect2()jFe Jeffrey Schiano 2014. All rights reserved. Rec 12. Problem 3 Solution10 Jeffrey Schiano 2014. All rights reserved. Rec 12. Problem 3 Solution11 Jeffrey Schiano 2014. All rights reserved. Rec 12. Problem 4• The input f(t) and zeros-state response y(t) of a LTI system is 1. Represent the system as a frequency response function H(jω)2. Represent the system as an ODE3. Represent the system as an impulse response h(t)12323() ()() 2 ()tttft e utyt e e ut Jeffrey Schiano 2014. All rights reserved. Rec 12. Problem 4 Solution13 Jeffrey Schiano 2014. All rights reserved. Rec 12. Problem 4 Solution14 Jeffrey Schiano 2014. All rights reserved. Rec 12. Problem 4 Solution15 Jeffrey Schiano 2014. All rights reserved. Rec 12. Problem 5• Consider the system and signal spectra shown below1. Sketch Y(ω)2. Sketch Z(ω)16()xtX1()H0cos(5 t)X2()H0cos(3 t)z( )ty( )t1()HX( )ooA5o3o5o3o12H( )3o3o1 Jeffrey Schiano 2014. All rights reserved. Rec 12. Problem 5 Solution17 Jeffrey Schiano 2014. All rights reserved. Rec 12. Problem 5 Solution18 Jeffrey Schiano 2014. All rights reserved. Rec 12. Problem 5 Solution19 Jeffrey Schiano 2014. All rights reserved. Rec 12. Problem 5 Solution20 Jeffrey Schiano 2014. All rights reserved. Rec 12. Problem 6• The following communication system generates a SSB signal s(t) from the baseband signal m(t) 1. Sketch the spectrum of the transmitted signal S(ω)21m( )tXcos( t)cs( )tM( )ULUL1cc1cU Jeffrey Schiano 2014. All rights reserved. Rec 12. Problem 6 Solution22 Jeffrey Schiano 2014. All rights reserved. Rec 12. Problem 6 Solution23 Jeffrey Schiano 2014. All rights reserved. Rec 12. Problem 6 Solution24 Jeffrey Schiano 2014. All rights reserved. Rec 12. Problem 7• The following receiver system recovers the baseband signal from the SSB signal s(t) generated in Problem 61. Sketch the required frequency response of the filter H(ω) 25s( )tXcos( t)cm( )tH( ) Jeffrey Schiano 2014. All rights reserved. Rec 12. Problem 7 Solution26 Jeffrey Schiano 2014. All rights reserved. Rec 12. Problem 7 Solution27 Jeffrey Schiano 2014. All rights reserved. Rec 12. Problem 7 Solution28 Jeffrey Schiano 2014. All rights reserved. Rec 12. EE 350Continuous-Time Linear SystemsRecitation 121 Jeffrey Schiano 2014. All rights reserved. Rec 12. Recitation 12 Topics2• Solved Problems – Fourier Transforms and properties– Application of Fourier Transforms Jeffrey Schiano 2014. All rights reserved. Rec 12. Problem 1• Consider the signal1. Sketch f(t)2. Determine, without computation of the spectra, whether the Fourier transform is an even function of frequency, an odd function of frequency, or neither3. Determine, without computation of the spectra, whether the Fourier transform is purely real, purely imaginary, or a complex-valued function of frequency3 Jeffrey Schiano 2014. All rights reserved. Rec 12. Problem 1 Solution4 Jeffrey Schiano 2014. All rights reserved. Rec 12. Problem 1 Solution5 Jeffrey Schiano 2014. All rights reserved. Rec 12. Problem 2• The Fourier transform of a signal f(t) is1. Determine, without computation of f(t), whether the signal f(t) is purely real, purely imaginary, or a complex-valued function of time2. Determine, without computation of f(t), whether the signal f(t) is an even function of time, an odd function of time, or neither6 Jeffrey Schiano 2014. All rights reserved. Rec 12. Problem 2 Solution7 Jeffrey Schiano 2014. All rights reserved. Rec 12. Problem 2 Solution8 Jeffrey Schiano 2014. All rights reserved. Rec 12. Problem 3• A signal f(t) has the Fourier transform1. Determine the energy of the signal f(t) using Parseval’stheorem2. Using an appropriate transform pair and property, determine f(t) 9 Jeffrey Schiano 2014. All rights reserved. Rec 12. Problem 3 Solution10 Jeffrey Schiano 2014. All rights reserved. Rec 12. Problem 3 Solution11 Jeffrey Schiano 2014. All rights reserved. Rec 12. Problem 4• The input f(t) and zeros-state response y(t) of a LTI system is 1.
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