High Pass Filter response by Fourier Transform

[Highlander-SP]

Whats the response by unit step input for the following High Pass Filter:

H(ω) = [ 1 – G2W(ω) ] . exp(-jωto)

x(t) = h(t)

X(ω) = F[x(t)] = πδ(ω) + 1/(j ω)

Y(ω) = X(ω).H(ω)

Y(ω) = [ πδ(ω) - πδ(ω). G2W(ω) + 1/(j ω) – G2W(ω)/(j ω)] . exp(-jωto )

y(t) = ?


where:
h(t) = step function (Heaviside)
π = pi
δ(ω) = delta Dirac in frequence domain
G2W(ω) = Gate function with 2W of band width
j = complex number = sqrt(-1)
to = constant time

Somebody can show step by step desenvolte the inverse Fourier transform?

thanks

 

[steve10]

Here you go.

 

[Highlander-SP]

Steve,

Thank you by that resolution!!

it look likes that you have the Lathi's Solution Manual for the 1st edition, and I need it very much, mainly for Filters, Fourier Transform and Amplitude Modulation.
Please, could you upload it here?

Thank you very much !!

ps.: What's the solution manual you have get that solution from?

 

[steve10]

I am sorry, Highlander-SP, that I don't have the manual you were talking about. Actually, I don't even know the book you refered to. Have you made your request in the ebook section? You can probably get help there.

 

[Highlander-SP]

Great Steve,

I had click in "help me" for you thanking your help, but i would like to know what's the solution manual you have get that solution from?

tks

 

[steve10]

I am glad that you think the solution has helped, Highlander-SP. But I don't really rely on any specific books, or I won't bother to answer the questions. That won't be interesting to me.