ABSTRACT We propose a new analysis methodology – FourIEr phase SpecTrum Analysis (FIESTA, or $\mathit {Φ }$ESTA) – for the study of spectral line profile variability in Fourier space. The philosophy of $\mathit {Φ }$ESTA is highlighted in its interpretation of a line deformation as various shifts of the composing Fourier modes. With this ability, $\mathit {Φ }$ESTA excels in distinguishing the effects of a bulk shift in a line profile, from changes in a line profile shape. In other words, it can distinguish a radial velocity shift due to orbiting companions like planets, from an apparent radial velocity shift due to stellar variability (often referred to as ‘jitter’). Most importantly, it can quantify the radial velocity impact of stellar jitter on each epoch. Our simulations show that (compared to a model that does not account for stellar activity), $\mathit {Φ }$ESTA can almost triple the fraction of planets recovered with orbital parameters measured to within 10 per cent of their input parameters, when extracting a 2 m s−1 amplitude planetary signal in the midst of ∼2 m s−1 amplitude starspot jitter for high signal-to-noise ratio (>200 pixel−1) data. $\mathit {Φ }$ESTA can also be used to identify stellar activity related periods in a periodogram analysis and classify relative amplitudes of stellar jitter and planetary signals, with examples for the analysis of HARPS data of the active star HD 224789 and the active planet-host star HD 103720. In the end, we demonstrate that $\mathit {Φ }$ESTA’s framework is working as well as other activity indicators in correlating with stellar jitter.