Pressure fluctuations are one of the most commonly measured parameters in studies of fluidized beds. Our work reveals that spectral analysis of pressure data requires more careful attention to sampling and analysis methods than are commonly employed by fluidization researchers. As a result, we call into question previous claims that scaling laws for fluidized beds have been validated through comparisons of pressure fluctuations between model and prototype beds. However, we have devised sampling and analysis protocols that accurately reveal the spectral features of fluidized beds and describe their dynamical character. Spectral analysis indicates that both bubbling and circulating fluidized beds behave as multiple, second-order dynamical systems. Using double probes, we have identified four prominent peaks (local maxima) in the spectra. These peaks are not the narrow spikes at discrete frequencies often associated with spectral analysis, but rather broad bands. They appear in both bubbling and circulating fluidized beds and show wide differences in their functional dependence on bed operating conditions. Our experiments suggest that they arise from global rather than local phenomena in fluidized media. Finally, using our sampling and analysis protocol, we compare the dynamics of model and prototype beds when the beds are operated under conditions of presumed hydrodynamic similitude.