Displaying Audio data in a Plugin


I currently have a plugin with a basic interface with sliders and knobs.

What I am looking to learn now is how to display audio in real-time in my interface. For example how to do a spectrum analyzer where the display curve of the spectrum is changing as the audio changes, or for example an equalizer where you have a line and points on the line to move up or down boosting or dipping frequencies.

Basically where should I start to learn how to display audio data for real-time plugins en general such as many default plugins that come with standard DAW’s do.
I appreciate any tips or info on this.
Thank you.

That might be helpful: