LTI system, Fourier transform, unit step function, sine wave

1. What is the Fourier transformation of sine wave?
2. What is the Fourier transform for unit step signal?
3. Does unit step function have Fourier transform?

What is the Fourier transformation of sine wave?

The Fourier Transform of the Sine and Cosine Functions

Equation [2] states that the fourier transform of the cosine function of frequency A is an impulse at f=A and f=-A. That is, all the energy of a sinusoidal function of frequency A is entirely localized at the frequencies given by |f|=A.

What is the Fourier transform for unit step signal?

Its Fourier transform is ˆH(ω)=1/(α+iω), which converges to 1/(iω) pointwise as α→0, except at ω=0.

Does unit step function have Fourier transform?

The unit step function does not converge under the Fourier transform.