What I am asking is a design or pulse shaping question.
We learn about analyzing circuits but not designing them in school.
Let's say I have an input signal which is a triangular wave and I want to generate some output signal with some sophisticated shape that are not simple sin or square wave or something we know.
How should we design the circuit in between to achieve that? What I can think of is to write equation of my output signal of desire in time domain somehow and take laplace of it to figure out what components in what order should be placed to achieve this signal.
Best Answer
The usual way to do this is to use store samples of the desired output waveform in a memory (EEPROM, for example), and feed them to a DAC at the correct rate, then filter the DAC output to remove aliasing effects.
With this arrangement the exact shape of the input waveform is irrelevant, provided you can derive a clean clock signal from it, and from that generate an appropriate (higher frequency) clock to drive the DAC.
Typically analog methods are only used when the desired output is something simple like the sine, square, or triangle waveforms you mentioned. Of course there may be special situations where you want to generate something more complex using analog methods, but the way to do it would then depend very much on the specific requirements that led you to need that complex waveform.