Recently I stumbled upon Fourier transforms which means I am very new to it. I've been given a question from my professor to find the inverse Fourier transform of a frequency spectrum which is given by:
I can go through each step to explain what I've done so far.
I know that omega is always positive, I rewrote the inverse fourier transform like this
Now the biggest equation is this - I can surely see that the signal seems to be in the complex form. I tried rewriting the exponential part in terms of sine and cosine function and then split the imaginary part and the real part. Is this the correct way to graph it? The equations which contain real part of the function and imaginary part are shown below
Also another thing I thought about is to find the magnitude of the complex function once I have real and imaginary part. Question is if this approach is correct. When I found the module of this function, I got this result (assuming that omega zero is equal to 1)