In the figure I don't see a different value for B. I see a phase shift (C is close to but less than pi/4) and decreased amplitude (A ~ 0.8). If you are interested in a changing frequency , then I suggest you look into the chirp function.
Edit: sorry, I only saw part a. If you want something like part b, it looks like there is coupling of some higher frequency behaviour with the phase of the original signal. That is, when the signal is at a peak or trough, there is some jitter/noise. It's not straightforward how to represent this, but you could try adding another signal composed of various noise (rand or randn) and step functions.