Eliminating the humming noise from a cheap SMPS
More than likely the problem is twofold.

In a two-pin SMPS adapter there can be a lot of high frequency common-mode noise on the output. This is due to the switching frequency being 100 kHz (or more) and the internal transformer coupling primary and secondary windings capacitively. So, in order to pass EMC regulations, a small capacitor is connected from the output DC circuit to the primary bus voltage. This is done to reduce that common-mode noise like this: -



If the SMPS used an earth pin at the AC socket then the more conventional approach would be to connect CY1 from the DC output to earth so, if you can find a better SMPS you might get better performance.

This capacitor does something else - it couples 100 Hz ripple on the primary DC bus to the secondary and this becomes a problem with sensitive audio circuits - you pick-up 100 Hz or 120 Hz hum.

The 2nd part of the problem is that a guitar is an unbalanced signal so any common-mode pick-up (hum from the SMPS) will asymmetrically couple to the input and its local 0 volt signal return and the result is that this hum will be amplified by any pedal units you have.

Linear AC adapters do not use high frequencies and therefore do not suffer from this problem as much.


  What Can I do to remove the humming noise from the cheap SMPS unit?


It is tricky to write an answer for that because some solutions will work on one particular set-up whilst others will work on a different set-up. Grounding the DC output (marked RTN on the picture above) is likely to have beneficial effects.