# Equation for half-damped triangle signal

I have triangle signal, which is damped only at the beginning of ramping phase (blue line in figure). I want to fit this type of signal. Just now I use symmetric equation, which gives me a damp at the end of ramping also:

$$y=C + \frac{A}{\pi}*\sum_{n=1}^{n=k}{\left[ {-1^n}\frac{\sin(2\pi nf(x-x_0))}{n}\right]}$$

Could You help me to find an equation which will give damping only from one side? Do you know similar signals? I will be good for me to read how to deal with them.

# To clarify:

I have a set of signals, which looks as blue line. I need to fit them. Signals has "damping" peak only at the beginning of ramping('wanted peak'). Solution I have, gives me also an "unwanted peak". I am searching for better solution. Which will gives me a green line, now i draw green by hand.

• You should explain the problem you are trying to solve instead of asking how to achieve what you think is the solution. Right now, it is hard to help you as you ask something specific with not much details and context. I would suggest 3 linear curves, but that is most likely not what you need... but how can we tell? – Pier-Yves Lessard Mar 2 '18 at 15:00
• Ah.. so it is probably nonlinear. Nevertheless, as data you can model it; but you must include cosine terms; or equivalently delay terms. Do you want a model that has the particular causality of a downward slope having an overshoot or push transient and not the positive slope? Or just an array of coefficients with no physical meaning? Actually, I am thinking of a motor where a switch is thrown and the motor spins up rapidly and then opened and the motor glides down; or some such. – rrogers Mar 6 '18 at 20:46
• Finding the peaks can be done by fitting a quadratic curve over the humps, or if the lines are straight then intersecting them would give turning points (but that's probably cheating to much). The presence of the overshoot is a problem I would presume intersecting the last two straight lines for the peak location and saying the negative excess could be called overshoot. The truth is that I think Wavelet analysis is the appropriate way to deal with this particular physical problem. Different tools for different jobs. – rrogers Mar 6 '18 at 20:55
• I think that's a great study/application. But unless you control the input ("watch my shiny watch go back and forth") I think Wavelets are the only robust tool to use. Unfortunately, there are problems. Beyond learning about them you need to select which particular one "fits"with the data variation; person to person. Perhaps somebody knows. We are being timed out on this discussion and I have to go; do you want to move to "discussion"? Unfortunately I don't have much to add and have to go for a while. – rrogers Mar 6 '18 at 21:06
• I suggest Daubech's book:Ingrid Daubechies: Ten Lectures on Wavelets, SIAM 1992. She was EE and the book is a good read. Motivation and theory nicely mixed! Wikipedia has a section which is brief and only covers a small part of the richness. – rrogers Mar 6 '18 at 22:11