Question

Find the Fourier transforms of this function.

h(t) = {1 if −3≤t≤0
{-1if 0 { 0 otherwise.

Answer 1

To find the Fourier transforms of the function h(t), we need to first rewrite the function in terms of the standard trigonometric functions.

Step-by-step explanation:

To find the Fourier transforms of the function h(t), we need to first rewrite the function in terms of the standard trigonometric functions.

For -3 ≤ t ≤ 0, the function is 1, which can be written as cos(0) since cos(0) = 1.

For 0 < t, the function is -1, which can be written as cos(π) since cos(π) = -1.

Since the function is 0 for any other values of t, we can ignore them in the Fourier transform. Therefore, the Fourier transform of h(t) is cos(0)U(-3,0) + cos(π)U(0,∞), where U(a,b) is the unit step function.