To get stable results, we need decoupling. This is needed both for the analog signals measured and for the reference used.
To be able to have a common reference for all signals measured over time, the voltage reference has to be exactly the same. To achieve this, the reference has to be decoupled with a large capacitor. For internal references this is not directly possible, but the AVCC and VCC have to be decoupled sufficiently. For both AVCC and for the external references, decoupling and filtering should be done. Using a filter inductor and a large capacitor will help keeping the reference stable. The larger the capacitor, the better stability is achieved. A 1 μF or larger capacitor is recommended. When using the ADC you have to wait until the capacitor is fully charged and stable, before any measurements can be done. The time until stable has to be calculated from the rise time of the RC connection of the capacitor.
For the analog signals, decoupling should also be done. When having single-ended signals, the decoupling should be done between the signal and ground and for differential signals the decoupling has to be between the positive and negative input. Decoupling of the signals is a more complex situation than the reference and this has to take the signals into account. If the signals are switching fast, the decoupling capacitor has to be lower. The decoupling capacitor should be as high as possible without changing the rise and fall time of the signal. It is therefore hard to give an exact value for the decoupling, and this has to be calculated as an RC circuit.