We performed intracellular recordings of relay neurons from the lateral geniculate nucleus of a cat thalamic slice preparation. We measured responses during both tonic and burst firing modes to sinusoidal current injection and performed Fourier analysis on these responses. For comparison, we constructed a minimal "integrate-and-fire-or-burst" (IFB) neuron model that reproduces salient features of the relay cell responses. The IFB model is constrained to quantitatively fit our Fourier analysis of experimental relay neuron responses, including: the temporal tuning of the response in both tonic and burst modes, including a finding of low-pass and sometimes broadband behavior of tonic firing and band-pass characteristics during bursting, and the generally greater linearity of tonic compared with burst responses at low frequencies. In tonic mode, both experimental and theoretical responses display a frequency-dependent transition from massively superharmonic spiking to phase-locked superharmonic spiking near 3 Hz, followed by phase-locked subharmonic spiking at higher frequencies. Subharmonic and superharmonic burst responses also were observed experimentally. Characterizing the response properties of the "tuned" IFB model leads to insights regarding the observed stimulus dependence of burst versus tonic response mode in relay neurons. Furthermore the simplicity of the IFB model makes it a candidate for large scale network simulations of thalamic functioning.