Problems with Noise
The voltage signal can be susceptible to electrical interference. Nearby equipment (especially equipment that has a heavy current requirement) may cause interference. Try turning nearby equipment off and see if the signal noise disappears.
Desktop computers, and old CRT (cathode ray tube) monitors are often sources of high frequency noise. Laptop computers and LCD displays are usually much quieter. It is normally good practice to position the computer and monitor away from the reaction vessel.
Mains powered equipment usually relies on the earthing of the power socket to also provide good grounding to the data recorder (and its shielding). However what constitutes a safe electrical earthing does not always provide good instrumental grounding and noise may actually be picked up on the earthing. Power sockets also grouped in various power circuits distributed throughout the laboratory building and each circuit usually has its own earthing that goes to a common ground. This means that moving the apparatus to a different power socket on a different circuit may improve your signal.
Avoid connecting your data recorder to a power strip/power board/power bar. Some of these do not provide electrical grounding (they certainly won't if their plug only has two pins). It's best to connect your data recorder directly into an electrical socket in the wall.
If the instrument you are connecting to the data recorder has a choice of analog outputs, use the analog output with the highest voltage. For example, a spectrophotometer might have an recorder output/integrator output of 10mV and 1V; you should use the 1V output.
The cable between the instrument and the data recorder should be shielded. The shield connector should be connected to either the ground on the instrument or on the data recorder, but not to both.
High frequency noise can be eliminated by selecting a suitable low-pass filter in Chart software. A 10 Hz low-pass filter will remove frequencies above 10 Hz (like the 50 Hz mains electricity noise for example), while letting pass frequencies below 10 Hz (like your peaks in many chemistry experiments). A high-pass filter can be used to eliminate signal drift. See this note which explains the difference between low-pass filters and high-pass filters.
Also see the application note covering problems with Noise in cyclic voltammetry and electrochemistry experiments.