Raspberry Pi 3 SPI speed and ADC sampling rate
Raspberry Pi is a poor choice for precise sampling unless you get a hard realtime system (like QNX) to run on it. If you're on Linux, you're running several dozen of tasks in parallel on only 4 CPU cores, and the task that reads the data is not even the highest priority, so there's very little confidence in the fact that your sampling rate is really 200Hz.

Increasing priority with nice can improve things, but it may not be enough. Consider using a dedicated unit (Arduino?) where you have full control over timing for acquisition, and transfer the properly acquired data to RPi or a laptop for analysis.

Another (unrelated) approach to noise reduction is oversampling: if you can get 2 kS/s instead of 0.2, and the noise is uncorrelated with the signal, averaging N samples will reduce the noise by \$\sqrt(N)\$.