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Mathematics - 3
Unit-1 Fourier series
Part-A
1. Find in the expa nsion of as a Fouri e r se rie s in
2. If is an odd func t ion de fined in , what is the val ue s of
and ?3. Find the Fouri e r cons ta n ts for in .
4. S tate Pa rseval s iden tity for the hal f rang e cosin e
expa nsion of in (0,1).5. Find the val ue of in the cosin e se rie
s expa nsion of in the in te rval (0,10).6. Find the roo t mea n
squ are of the func tion in the in te rval .7. D ete rm ine in the
Fouri e r se rie s expa nsion of .
8. D
e fine roo t mea n squ are val ue of a func t ion in .9. If in
the in te rval (0,4), the n find the val ue of in the Fouri e r se
rie s expa nsion .10. The Fouri e r se ries expa nsion of in is .
Find the roo t mea n squ are val ue of
in the in te rval
Part-B
11. Find the Fouri e r se ries for
12. Find the Fouri e r se ries for . He nce find 13. Ob ta in
the hal f rang e cosin e se rie s for .14. Find the hal f rang e
sin e se rie s for in the in te rval and deduc e that 15. Find the
hal f rang e cosin e se ries of in the in te rval . Henc e find the
su m of
the se rie s 16. Find the Fouri e r se ries of pe riodici ty 3
for 17. Find the complex for m of the Fouri e r se rie s for the
func t ion in the in te rval (-1,1).18. Find the Fouri e r se ries
up t o second ha rmonic for the fo llow ing data
0 1 2 3 4 5
9 18 24 28 26 2019. Find the Fouri e r se ries up t o second ha
rmonic for the fo llow ing data
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0 /3 2
1.0 1.4 1.9 1.7 1.15 1.2 1.020. Find the Fouri e r se ries up t
o second ha rmonic for the fo llow ing data
0 360
0.8 0.6 0.4 0.7 0.9 1.1
0.8------------------------------------------------------------------------------------------------------------------------------------------
Unit-2 Fourier Transform
Part-A
1. W rite the Fouri e r transfor m pa ir.2. S tate the Fouri e r
in te gral the or em.
3. Find Fouri e r transfor m of
4. Find Fouri e r Sine t ransfor m of 5. W hat is the Fouri e r
transfor m of if the Fouri e r transfor m of is .6. S tate the
Fouri e r transfor ms of the de rivat ive s of a func tion .
7. Pro ve that .8. Find the Fouri e r cosin e t ransfor m of de
fined as
9. Pro ve that
, whe re .
10. S tate the con vo lu tion the or em of the Fouri e r
transfor m s.
PART-B
11. Find the Fouri e r transfor m of and he nc e deduc ethe val
ue of and .
12. Find the Fouri e r transfor m of and he nc e deduc ethat
.
13. Find Fouri e r Cosin e t ransfor m of and he nce find Fouri
e r sin e t ransfor m of .14. U se t ransfor m s meth od to eval
uate .
15. Find the Fouri e r Sine t ransfor m of the func t ion .16.
Find the Fouri e r transfor m of . He nce deduc e that .
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17. By finding the Fouri e r cosin e t ransfor m of and using Pa
rseval s iden t ity for cosin e t ransfor m eval uate .
18. So lve for fro m the in te gral e qu at ion
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Unit-5 Z Transform
1. Find in Z-transform .
2 . Find using Z-transform . 3 . S tate and prove initial value
theorem in Z-transform . 4 . Find the Z-transform of . 5 . Find the
Z-transform of (n+2) . 6 . S tate the final value theorem in
Z-transform .
7 . Find .
8 . E valuate .
9 . Ex press in terms of . 10. Find the value of when . 11. Form
the difference equation from . 1 2 . Form a difference equation by
eliminating arbitrary constants from . 1 3 . P rove that . 1 4 . S
tate and prove the second shifting theorem in Z-transform . 1 5 .
Find using partial fraction .
1 6 . S olve the difference equation.
1 7 . U sing convolution theorem evaluate inverse Z-transform of
.
1 8 . U sing Z-transform solve given that. 1 9 . Find by using
method of partial fraction .
20. U sing Z-transform solve difference equation given that. 21.
Find the inverse Z-transform of .
22 . U sing convolution theorem find .
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23 . S olve the difference equation given that , by the method
of Z-transform . 24 . Find the inverse Z-transform of by partial
fraction method .
25 . Find the Z-transform of and .
26 . Find the inverse Z-transform of by using convolution
theorem .
27 . S olve given , using Z-transform . 28 . Find the inverse
Z-transform of .
29 . D rive the difference equation, given where A and B
arearbitrary constants . 30. V erify initial and final value
theorem for .
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