1) I am supposed to verify that this IS orthogonal:

x1(t) = ej∏t

x2(t) = e-j∏t on the interval [0,1]

I know that I am suppose to ∫x1(t)x2(t) oner 0,1

However, when I multipy x1 and x2 they become 1. Integrating 1 over [0,1] gives the value of 1.

// I know I am supposed to get zero.

So where have I done wrong?

Q2) I have difficulty find the period of this function

x(t) = 0.5 + cos∏t + 2 sin[1.5∏t + ∏/4 ]

I know that I am suppose to use T= 2∏/ω to find period

Thus the period of cos ∏t is 2

and that of sin[1.5∏t + ∏/4] is 4/3

I assume that 0.5 does nothing to the equation.

My prof mentioned that the period is 4. How can this be?

Q3) Can anyone explain how to START doing this q :

find the TFS of x(t) = Ʃ[δ(t-3n) + δ(t-1-3n)] //from n=- ∞ to ∞

Just tell me how to integrate the the delta function with an n.

I didnt understand my prof..

Q4) x(t) = ∞ n=-∞ Ʃy(t-3n) where y(t) = e-t, 0<=t<=3, 0 otherwise

a) Find complex fourier series of x(t)

b) Plot double sided amplitude and phase spectrum of x(t)

For a I got the answer as ck = (1-e^-3(1+j(2∏/3))) / 3(1+j(2∏k/3))

However, I dont know why my professor threw away the imaginery part

Thanks.

x1(t) = ej∏t

x2(t) = e-j∏t on the interval [0,1]

I know that I am suppose to ∫x1(t)x2(t) oner 0,1

However, when I multipy x1 and x2 they become 1. Integrating 1 over [0,1] gives the value of 1.

// I know I am supposed to get zero.

So where have I done wrong?

Q2) I have difficulty find the period of this function

x(t) = 0.5 + cos∏t + 2 sin[1.5∏t + ∏/4 ]

I know that I am suppose to use T= 2∏/ω to find period

Thus the period of cos ∏t is 2

and that of sin[1.5∏t + ∏/4] is 4/3

I assume that 0.5 does nothing to the equation.

My prof mentioned that the period is 4. How can this be?

Q3) Can anyone explain how to START doing this q :

find the TFS of x(t) = Ʃ[δ(t-3n) + δ(t-1-3n)] //from n=- ∞ to ∞

Just tell me how to integrate the the delta function with an n.

I didnt understand my prof..

Q4) x(t) = ∞ n=-∞ Ʃy(t-3n) where y(t) = e-t, 0<=t<=3, 0 otherwise

a) Find complex fourier series of x(t)

b) Plot double sided amplitude and phase spectrum of x(t)

For a I got the answer as ck = (1-e^-3(1+j(2∏/3))) / 3(1+j(2∏k/3))

However, I dont know why my professor threw away the imaginery part

Thanks.

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