Pressure fluctuation signals measured from four different axial locations in a bubbling bed 0.3 m in diameter and 3 m in height were analyzed using multiple approaches, including wavelet transform, Hurst analysis, multiscale resolution, and time-delay embedding. After examining decomposition residuals using different compact support Daubechies wavelets, the Daubechies second-order wavelet was chosen as an optimal wavelet for decomposing pressure signals. Hurst analysis of the decomposed signals shows that the measured pressure fluctuations can be resolved to three characteristic scales: bifractal mesoscale signals with two distinct Hurst exponents; monofractal micro- and macroscale signals with only one characteristic Hurst exponent. Energy profiles of the three scale components confirm that the measured pressure signals mainly reflect the mesoscale component. Time-delay embedding analysis of three scale signals demonstrates that the microscale dynamics is more complex than the mesoscale dynamics, and the mesoscale dynamics is more complex than the macroscale dynamics. That this result cannot be found solely from Hurst analysis shows the importance of integrating multiple approaches for characterizing the complexity of fluidized systems.