Its a top-down intro to Fourier transforms that explains the derivation of the transform and why there are complex numbers involved, etc. Starts out very basic and top level, but covers all the important little details by the end.
https://www.cec.uchile.cl/cinetica/pcordero/MC_libros/Numeri...
If it's in an applied area, like calculus or statistics, there are usually plenty of books that skip the theory and simply give you recipes to use. If it's a more theoretical area then the theory is presumably why you came, so of course they aren't going to skip it. It's also common to study application-style first, then theory later. So first you take "calculus", then "intro to analysis" which is the same topics as calculus but with the proofs done carefully, and then a more theoretical and abstract approach to analysis.
If you start with an abstract textbook, you'll see a bunch of definitions and axioms at the beginning that might make the book feel self-contained like you can start from nothing, but in practice you are supposed to know the basics of the topic before you start such a book. Otherwise you will have a hard time. That might be the difficulty you've encountered.
More like this:
Here is a tool you can use to perform these many tasks in these many situations. Now that you have seen how it works, let us investigate why it works and where does it come from (maybe with a bit of history). Because stories are always easier to remember.