While it is impossible to eliminate noise in an accelerometer measurement system, there are steps you can take to reduce noise to a manageable, or acceptable, level. I'll attempt to break this issue down to illustrate.
First, there is intrinsic noise, which is noise generated by the system's electrical, electronic and sometimes mechanical components themselves. This is the type of noise controlled (by design) and specified by the accelerometer and instrument manufacturer in their datasheets. There is nothing that you, as a user, can do to reduce this type of noise. You can only select the appropriate instrumentation that meets your intrinsic noise performance needs in your application.
Second, there is extrinsic noise, which is noise originating from external sources to the measurement system. This is the type of noise that the user can control, to some degree, by utilizing Best Practices techniques in installing and using the accelerometer measurement system. This is the key for you, the user, to reduce noise in your system.
External sources of noise come in a variety of forms, but most commonly take the form of capacitively coupled noise, magnetically coupled noise and current coupled noise. See Endevco TP 270 for a fuller explanation of each of these. Capacitively coupled and magnetically coupled noise are more commonly known as 60/50 Hz interference, radio frequency interference (RFI), etc. We live in an electrically rich world, and these interferences are unavoidable.
Capacitively coupled noise can usually be minimized by use of shielded cable, either coaxial type or shielded, twisted pair type. These are very commonly available today from many manufacturers, and can be utilized easily.
Magnetically coupled noise is more difficult to shield. Careful consideration should be given to how the instrumentation system is installed. Cables should not be run in close proximity to AC power lines, or large magnetic devices, such as electric motors and transformers. Cable runs should be kept as short as possible, with a minimum of loops and turns used. In extreme cases, where magnetic sources are unavoidable, you may have to install the cable inside grounded, metal conduit. For piezoelectric accelerometers, consider the use of a remote charge converter (RCC), such as Endevco's model 2771C. This device converts the interference susceptible charge signal into a more robust voltage signal, allowing you to run longer cables if needed.
Current coupled noise is the result of ground loops. Ground loops are a result of multiple grounding points in the measurement system. Despite the name "ground", not all grounding points are at the exact same voltage potential. Thus, if you have more than one grounding point, you will have current flow between the different potentials, resulting in additional noise. The solution is to make sure you are grounding at only one point, known as the single-point ground. Endevco recommends grounding at the signal conditioner. Many accelerometers are case grounded (meaning their outer surface is electrically connected to ground), making it difficult to achieve a single-point grounded system. In this case, you should use an isolated mounting stud with the accelerometer. These types of mounting studs are designed to electrically isolate the accelerometer from the surface it is being mounted to.
As always, contact your Endevco Applications Engineer if you have further questions.