Removing digital noise on quadrature encoder signals
Looking at signals from a logic analyzer (especially where noise is a factor) can be confusing. It's possible that the noise you see is not at the same level as your quadrature signals, but because the analyzer either sees a signal over the logic threshhold or not, they look to be the same amplitude as your desired signal. 

I'd suggest firstly that you check you have at least 10-20 uF on the supply voltage to the Quadrature detector. They can be sensitive to voltage fluctuations if you are using them near their bottom limit of supply voltage. Most are designed for 5-12 or 12-24 V supplies, but some are specified as 5 V only (and usually quite a different design). If you are using 5 or 12 V you are right on their lower limit for each variant.

Make sure the A, B, Z signals have a Schmitt trigger receiver such as the 74LS14, and check the datasheet for your Quadrature detector to see if it expects a pullup resistor at the receiver end of the cable (most do)....conversely, if you do have a pullup resistor make sure it's not too low a value. 

As an example here is the datasheet for an Omron Rotary Encoder: http://www.mouser.com/ds/2/307/e6b2-c_ds_csm491-25665.pdf

Notice that the I/O structure varies considerably for the variants; pulldown, pullup and line drivers.