Derivative of signal is normally distributed - why? I stumbled upon something while analyzing some of my data and don't know the answer to this. There seems to be some sort of drift in my measurement system and I wanted to know more about it. I measured a signal with some amplitude and phase as given in the image below. Now, when I take the derivative of either amplitude or phase and take the histogram of it, the result is normally distributed. What does that mean? I have little background in statistics, and appreciate any source that you could also provide on this.
Thank you very much.

 A: You are seeing what you are supposed to see, as per the comment by @Aksakal. I put together a little simulation model to try to duplicate what you had in the left images, ignoring scale factors and units. This is shown in the figure below:

The raw temporal output is the sum of 1) the step response of a simple RC low pass filter, 2) a sinewave and 3) Gaussian white noise. The simulation step size was 1 ms and all other parameters are shown on the figure. The raw response (black), plus the differentiated response (red), are shown on the next figure:
 
Then I ran the simulation 1000 times and binned the resulting 4,096,000 values from the differentiated response. The histogram is shown in the final figure:

So this is just a matter of linearity.
A: @EdV's answer provides a very standard constructed model that has a Gaussian/Normal error term, which is a very common model for time series. 
A very natural question might be why is the error term Gaussian? To be clear, it's frequently not! But when it does occur, a natural explanation is something like the central limit theorem. This theorem1 tells us that if we have a random variable that is the average of many independent random variables, the distribution of this average will approach a normal distribution asymptotically, even if the individual variables are not normal distributed themselves. I'm doing a little handwaving here, but if the noise in your recordings are the result of a summation of a large number of much smaller errors of all roughly the same magnitude, it would make sense that this observed noise would be approximately normally distributed.
1 Actually there are many, many different versions of the central limit theorem out there that apply under different conditions. The central limit theorem I'm referring to is the one they teach in stats 101. 
