Fourier Transform of x(t) and g(t) with Product Calculation

[nikki92]

Homework Statement

x(t) = 5cos(2*pi*1000*t) and g(t) = ∑ from n=-infinity to infinity delta(t-n/10000)

find Fourier transform of x(t) and g(t) and the product of the two

The Attempt at a Solution

x(w) = 5*sqrt(pi/2) [delta(w-2000pi)+delta(w+2000pi)]

g(w) = 1

so would the product of the two just be the x(w) ?

 

[vela]

Homework Statement

x(t) = 5cos(2*pi*1000*t) and g(t) = ∑ from n=-infinity to infinity delta(t-n/10000)

find Fourier transform of x(t) and g(t) and the product of the two

The Attempt at a Solution

x(w) = 5*sqrt(pi/2) [delta(w-2000pi)+delta(w+2000pi)]

g(w) = 1

so would the product of the two just be the x(w) ?

$G(\omega)$ isn't equal to 1. That's the Fourier transform of a single delta function. You have a train of delta functions.