doubt regarding impulse function

[purnapragna]

hi i have a doubt like

i have a CT periodic impulse train whose period is 'T ' and as known it FT is again

periodic impulse train. Now if i make 'T' tends to '0'(zero) what will be the time

domain signal i.e., how can you define the signal in time domain and what will be

its corresponding FT?

thank you

purna

 

[khubaibahmed]

Sorry for saying it to be a funny Question.As period of impulse train approaches to zero then all the impulses will superimpose and diverge to infinity.and once again it FT will be a funny thing

 

[purnapragna]

i dont think it is a funny question and i think it is just a dual of the Fourier Transform of the impulse.

all the impulses will converge does not mean they will diverge

thnx


purna

 

[b.pricope]

As I see it it's like this:
x(t) = sum(dirac(t-kT),k,-inf,inf) Now:
lim(x(t),T,0) = sum( lim(dirac(t-kT),t,0), k,-inf,inf) = sum(dirac(t),k,-inf,inf) =
= dirac(t)*sum(1,k,-inf,inf)=dirac(t) which has FT = 1
I am unsure about the last step however.

 

[brahma]

for your information if u take FT of a impulse function it will be a DC signal( that is a constant magnitude) so no matter even if take FT of impulse train it will give the same result.

 

[b.pricope]

For your information: check the fourier transforms tables.
FT ( diract(t) ) = 1 ...true
FT (impuls train with period T) = impuls train in frequency domain with period 2pi/T and scaled with amplitude 2pi/T

What I said in the previous reply is correct!