At present most laser systems for generating phase-stabilized high-energy pulses are chirped pulse amplifier systems that involve the selection and subsequent amplification of pulses from a phase-stabilized seed oscillator. We investigate the effect of the picking process on the carrier envelope phase stability and how the phase noise of the picked pulse sequence can be estimated from the phase noise properties of the seed oscillator. All noise components from the original pulse train above the picking frequency are aliased into the picked pulse train and therefore cannot be neglected.