First, take into account that you will get a different set of equations for each block of samples, unless you are dealing with a short looped sample.
I have found this to be a very detailed explanation: https://www.youtube.com/watch?v=B2iUDBZzBpY&t=1474s&ab_channel=DavidDorran
And there's also the free course here: https://www.coursera.org/specializations/digital-signal-processing