a signal x(t) has X(w)={1for |w|<}W then x(t) crosses zero first time at what t ?

Question

X(w) is the fourier transform of x(t). in time domain x(t) is a sinc function.

Answer 1

Sounds like a homework problem, so I'm going to assume you have a textbook in front of you. Like you said x(t) is a the sinc function. This is a standard transform pair, so find the formula for the corresponding sinc function.

It's going to be something like sin ( pi * K * t) / (pi * K * t) ... i don't remember exactly. The K is there to make the math work, i.e. the energy in the frequency domain must equal the energy in the time domain.

The first time it equals 0 is when sin ( pi * K * t) equals zero, t not equal 0. so whenever K*t = 1.