Im reading Will Pirkles Designing audio effect plugins book and I'm not sure if I'm understanding the z transform correctly. I got up to differential equations in college, but haven't done math in over half a decade, so hopefully learning DSP isn't way, way over my head.
As I'm understanding the books explanation: the z transform changes formulas to be in terms of z, the complex sinusoid. z, when mapped from inputs of 0-pi, will output frequencies from 0hz to Nyquist. Assuming this is correct, then:
Will any one of these different complex frequencies (from 0hz to Nyquist) have a different phase from any other frequency within that range?
Is a z itself a function, with a specific z value basically just being a specific one of these complex frequencies (again, each with unique phase)?
I assume that since it's possible to create an audio oscillator at a certain frequency and adjust it's phase however I want, that the "unique phase" thing I'm assuming is correct with the complex sinusoid doesn't limit the phase of real output, does it? (i.e. if there's an audio application where the complex sinusoid is outputting a complex frequency with 11khz with 90degree phase, it doesn't mean that an audio frequency 11khz tone coming from my speakers is required to have a specific phase, right?)
Hopefully any of that made any sense. I'm sure any correction of any part of what I wrote will be helpful. If it sounds like I have absolutely no clue what I'm talking about please ELI5. Thank you kindly to anyone that replies.