Q.7 Consider the finite-duration signal f (t) given in Fig.3. a) Evahate the Fourier transform F(jn) of f(t) and show that sin F(jn) = 1 Fig.3 2 -12 0 /2 Using the relation between F(jn) and c, , evahuate c, for the periodic signal given in Fig 4. Periodic Periodic -t/2 0 v2 To Fig.4 b) If 2=N ,where N is an integer, show that c, =0 for k =mN for m==1, ±2, ±3 . For N= 3 plot c, Using the reation between a, and e , ie. a, = co. az = 2||. = arg{c}, express f,(t) as a sum of real simusoidal signals and write the sum explicitly up to and inchuding the 5th term

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Q.7
Consider the finite-duration signal f (t) given in Fig.3.
a)
Evahate the Fourier transform F(jn) of f(t) and show that
sin
F(jn) = 1
Fig.3
2
-12
0 /2
Using the relation between F(jn) and c, , evahuate c, for the periodic signal given in
Fig 4.
Periodic
Periodic
-t/2
0 v2
To
Fig.4
b) If
2=N ,where N is an integer, show that c, =0 for k =mN for
m==1, ±2, ±3 . For N= 3 plot c, Using the reation between a, and e ,
ie. a, = co. az = 2||. = arg{c}, express f,(t) as a sum of real simusoidal
signals and write the sum explicitly up to and inchuding the 5th tem
Transcribed Image Text:Q.7 Consider the finite-duration signal f (t) given in Fig.3. a) Evahate the Fourier transform F(jn) of f(t) and show that sin F(jn) = 1 Fig.3 2 -12 0 /2 Using the relation between F(jn) and c, , evahuate c, for the periodic signal given in Fig 4. Periodic Periodic -t/2 0 v2 To Fig.4 b) If 2=N ,where N is an integer, show that c, =0 for k =mN for m==1, ±2, ±3 . For N= 3 plot c, Using the reation between a, and e , ie. a, = co. az = 2||. = arg{c}, express f,(t) as a sum of real simusoidal signals and write the sum explicitly up to and inchuding the 5th tem
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