The absolute best teaching of the Fourier transform I've ever encountered is the extremely bizarre book "Who is Fourier?"

https://www.amazon.com/Who-Fourier-Mathematical-Transnationa...

Try this remarkable book:

Who Is Fourier?: A Mathematical Adventure

https://www.amazon.com/Who-Fourier-Mathematical-Transnationa...

It started off as a bunch of non-math literate folks teaching themselves math from scratch, including trigonometry, calculus etc, and ending in Fourier series. It is a very approachable and fun book.

Just the book for you:

"Who is Fourier: a mathematical adventure" https://www.amazon.com/Who-Fourier-Mathematical-Transnationa...

It is a simply brilliant book that takes you from basic trigonometry, logarithms and so on through calculus and finally fourier series.