  We introduce a new method for analysing the aperiodic variability of coherent
pulsations in accreting millisecond X-ray pulsars. Our method involves applying
a complex frequency correction to the time-domain light curve, allowing for the
aperiodic modulation of the pulse amplitude to be robustly extracted in the
frequency domain. We discuss the statistical properties of the resulting
modulation spectrum and show how it can be correlated with the non-pulsed
emission to determine if the periodic and aperiodic variability are coupled
processes. Using this method, we study the 598.88 Hz coherent pulsations of the
accreting millisecond X-ray pulsar IGR J00291+5934 as observed with the Rossi
X-ray Timing Explorer and XMM-Newton. We demonstrate that our method easily
confirms the known coupling between the pulsations and a strong 8 mHz QPO in
XMM-Newton observations. Applying our method to the RXTE observations, we
further show, for the first time, that the much weaker 20 mHz QPO and its
harmonic are also coupled the pulsations. We discuss the implications of this
coupling and indicate how it may be used to extract new information on the
underlying accretion process.
