We present a new parametric autocovariance kernel function for characterizing properties of the mesoscale eddy field and the non-phase-locked internal tide from ocean time series records. We demonstrate that the model captures the important spectral properties, namely the spectral roll-off of the mesoscale continuum and the broad spectral “cusps” centered around the tidal forcing frequencies. The spectral cusp model has three main parameters that characterize the non-phase-locked internal tide: the amplitude, a decorrelation timescale and a shape parameter that captures the rate at which the cusp rolls away. Estimation of the third shape parameter is novel. We argue that an integral timescale is the most suitable characteristic timescale and show how it relates to the parametric decorrelation timescale. A key innovation of this work is that we estimate the parameters in the frequency domain using the debiased Whittle likelihood, thus avoiding the computational demands of estimating the autocovariance in the time domain. We apply our spectral parameter estimation technique to output from idealized and realistic numerical experiments of internal tides propagating through a mesoscale eddy field. We robustly demonstrate that both the non-phase-locked amplitude and integral timescale are influenced by the amplitude of the mesoscale flow field. Furthermore, we reveal that the integral timescale is set by global properties of the eddy field, whereas the shape of the spectral cusp is set by its local properties. The semi-diurnal integral timescale, calculated from a 12-month long, realistically forced ocean basin experiment, was 5–7 d and relatively constant in space.