We present a comprehensive analysis of long-term periodic variability of Cyg X-1 using the method of multiharmonic analysis of variance applied to available monitoring data since 1969 , in X-rays from Vela 5B , Ariel 5 , Ginga , CGRO and RXTE satellites and in radio from the Ryle and Green Bank telescopes .
We confirm a number of previously obtained results , and , for the first time , find an orbital modulation at 15 GHz in the soft state and show the detailed non-sinusoidal shape of that modulation in the hard state of both the 15-GHz emission and the X-rays from the RXTE /ASM .
We find the CGRO /BATSE data are consistent with the presence of a weak orbital modulation , in agreement with its theoretical modelling as due to Compton scattering in the companion wind .
We then confirm the presence of a \sim 150-d superorbital period in all of the data since \sim 1976 , finding it in particular for the first time in the Ariel 5 data .
Those data sets , covering > 65 superorbital cycles , show a remarkable constancy of both the period and the phase .
On the other hand , we confirm the presence of a \sim 290-d periodicity in the 1969–1979 Vela 5B data , indicating a switch from that period to its first harmonic at some time \la 1980 .
We find the superorbital modulation is compatible with accretion disc precession .
Finally , we find a significant modulation in the RXTE /ASM data at a period of 5.82 d , which corresponds to the beat between the orbital and superorbital modulations provided the latter is prograde .