Tagore Engineering College Department of Electrical and Electronics Engineering EC 2314 Digital Signal Processing University Question Paper Part-A
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1 Tagore Egieerig College Departmet of Electrical ad Electroics Egieerig EC 34 Digital Sigal Processig Uiversity Questio Paper Part-A Uit-I. Defie samplig theorem?. What is kow as Aliasig? 3. What is LTI system? 4. State samplig theorem. 5. What are the classificatio of sigals? 6. What are eve ad odd sigals? 7. State the advatages of Digital sigal processig over aalog sigal processig. 8. Determie the Nyquist rate for the followig sigal x(t= +cos000πt-si500πt. 9. Determie whether the sigal x( j e ( 4 is a eergy sigal or a power sigal. Uit-II. Metio the relatio betwee, Z trasform ad Fourier trasform. Give ay two properties of liear covolutio? 3. Fid the z-trasform of a A discrete impulse b A discrete step. 4. What is mea by ROC i Z-trasform? 5. Write the commutative ad distributive properties of covolutio. 6. What is ROC of z-trasform? state its properties. 7. Defie Discrete-Time Fourier Trasform for discrete sequeces 8. Fid the Fourier Trasform of the sigal x(=u( 9. Write the DTFT for, a x( a u( b x( 4 ( 3 ( - 0.Obtai the Discrete Fourier series coefficiets of x( =cos w.what is the z-trasform of discrete uit step fuctio?.fid the Z-trasform of the sequece 3.Determie the discrete time Fourier trasform of the sequece x(={,-,,-}. 4.Give x( {,,3,4 } ad h ( {, }. Fid the respose y( ( x {,,, } 5.Give x(=δ(-. Determie the z-trasform ad its ROC.
2 Uit-III. Calculate DFT of x(={,,-, -}.. Differetiate betwee DIT-FFT ad DIF-FFT? 3. Draw the basic butterfly diagram for Radix DITFFT. 4. What is FFT? What its advatage? 5. Fid the 4-poit DFT of sequece x(={,}? 6. Distiguish betwee liear covolutio ad circular covolutio. 7. Defie circular covolutio. How ca oe obtai liear covolutio usig it? 8. Why the computatio of FFT is said to be i place? 9. Give x(={,,3,4}. What is the circularly shifted sequece x(-? Part B Uit-I i Check whether the followig is liear, time ivariat, casual ad Stable y ( x( x( Check whether the followig are eergy or power sigals. x( u( x i Describe i detail the process of samplig ad quatizatio. jw o ( Ae Check whether the followig are periodic x( cos(3 x( si(3 3 i What do you mea by Nyquist rate? Give its sigificace.
3 Explai the classificatio of discrete sigal. 4 i Explai i detail the Quatizatio of digital sigals Describe the differet types of samplig methods used 5 i Discuss whether the followig are eergy or power sigals 3 x( u( x( Ae jo Explai the cocept of quatizatio. 6 Check whether followig are liear, time ivariat, causal ad stable y ( x( x( y( cos x( 7 i What is causality ad stability systems? Derive the ecessary ad sufficiet coditio o the impulse respose of the system for causality ad stability Determie the stability for the followig systems 3 y ( x( k 0 4 k k k y ( x( k k 0 8 i What is meat by eergy ad power sigal? Determie whether the followig sigals are eergy or power or either eergy or powe sigals. x ( u( x ( si 6 [Dec-0] ( 3 x 3 ( j 3 6 e 4 x ( e u( 4 What is meat by samplig? Explai samplig theorem. (04
4 [Dec-0] Uit-II i Determie the Z trasform of x( a cos u( o (05 (03 x( 3 u( Obtai x( for the followig X 0.5z ( z.5z ROC: z >, z <0.5, 0.5< z <. i Determie the liear covolutio of the followig sequeces x ( {,,3, } x ( {,,, } Obtai the system fuctio ad impulse respose of the followig system y ( 5y( x( x(. 3 i Explai the properties of Z-trasform. Fid the impulse respose give by differece equatio y ( 3y( 4 y( x( x( 4 i Test the stability of give systems y( cos( x( y ( x( 3 y( x( Fid the covolutio. x ( {,,, }, h( {0.5,,,,0.75} 5 i Obtai the liear covolutio of x ( {3,,,}, h( {,,,}. A discrete time system is described by the followig equatio
5 y ( y( x( x(, Determie its impulse respose. 4 6 i Obtai the discrete Fourier series coefficiets of x( cos (04 o Determie x( for give trasferfuctio 3z ( X ( z with ROC: z >, z < 3z z 7 i Fid the z-trasform ad its ROC of x( u( 5 u( 5 A system is described by the differece equatio y( y( 5x(. Determie the solutio, whe the iput x( u( ad the iitial coditio is give by y(-=, usig Z 5 trasform 8 i Determie the impulse respose of the system described by the differece equatio y( y( y( x( x( usig Z trasform ad discuss its stability/ [May-0] Fid the liear covolutio of x( {,4,6,8,0 } with h ( {,3,5,7,9 } [May-0] Uit-III i Explai the followig properties of DFT. Covolutio Time shiftig 3 Cojugate Symmetry. Compute the 4 poit DFT of x ( {0,,,3 }. i Explai the Radix DIFFFT algorithm for 8-poit DFT Obtai the 8 poit DFT usig DITFFT algorithm for
6 x ( {,,,,,,,} 3 A 8 poit sequece is give by x ( {,,,,,,, }. Compute the 8- poit DFT of x( by radix- DIT-FFT method also sketch magitude ad phase. (6 4 Determie the respose of LTI system whe the iput sequece is x( {,,,, } usig radix DIF FFT. The impulse respose is x ( {,,,}. (6 5 i Explai 8 pt DIFFFT algorithm with sigal flow diagram. Compute the DFT of x ( {,,0,0 } 6 i Describe the followig properties of DFT. Time reversal Circular covolutio Obtai the circular covolutio of x ( {,,,} x ( {,,3, } 7 i State ad prove covolutio property of DFT Fid the iverse DFT of X ( k {7, j, j, j,, j, j, j } [May-0] 8 i Derive decimatio-i-time radix- FFT algorithm ad draw sigal flow graph for 8-poit sequece. Usig FFT algorithm, compute the DFT of x ( {,,,,,,, } [May-0]
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