# Need help on signals and systems, Fourier representation of a signal

I've got a homework question for my signals and systems class.

In the question, we're given the graph of the magnitude and the phase of a continuous signal. Here are the graphs:

I have to find the real continuous function x(t) based on the magnitude and phase given.

I found this formula on the internet:

I figure I just need to find the function for the magnitude and phase then I insert it into the formula to figure out the real continuous signal.

My problem is that I'm confused as to how to find the function for the magnitude and phase.

I figured out how to find the function for the magnitude, but I still don't know if it's correct or not:

As you can see, I already wrote the function for |X(jw)|, but I haven't figured out the function for the phase. For the function |X(jw)|, I figured it out from this formula:

To sum up:

1. Am I already on the correct path to find the real continuous signal x(t)?
2. If I'm already on the correct path, how do I find the function for the phase?
3. Is the function for the magnitude already correct?
• Is this an electrical engineering question? Commented Apr 25, 2023 at 13:48
• I think so. It's for a signals and systems class which correlates a lot with telecommunications, a subdiscipline of electrical engineering. Commented Apr 25, 2023 at 13:53

In order to find the function of the the phase, assuming its slope is linear of course, use the start and end points: $$(-2,\pi/2), (2, -\pi/2)$$