Sunspots are intense regions of magnetic flux that are rooted deep below the photosphere. It is well established that sunspots host magnetohydrodynamic waves, with numerous observations showing a connection to the internal acoustic (or p-)modes of the Sun. The p-modes are fast waves below the equipartition layer and are thought to undergo a double mode conversion as they propagate upward into the atmosphere of sunspots, which can generate Alfvénic modes in the upper atmosphere. We employ 2.5D magnetohydrodynamic numerical simulations to investigate the adiabatic wave propagation and examine the resulting power spectra of coronal Alfvénic waves. A broadband wave source is used, which has a 1D power spectrum mimicking aspects of the observed p-mode power spectrum. We examine magnetoacoustic wave propagation and mode conversion from the photosphere to the corona. Frequency filtering of the upwardly propagating acoustic waves is a natural consequence of a gravitationally stratified atmosphere and plays a key role in shaping the power spectra of mode-converted waves. We demonstrate that the slow and fast magnetoacoustic waves and Alfvén waves above the equipartition layer have similarly shaped power spectra, which are modified versions of the driver spectrum. Notably, the results reveal that the coronal wave power spectra have a peak at a higher frequency than that of the underlying p-mode driver. This matches observations of coronal Alfvénic waves and further supports the role of the mode conversion process as a mechanism for Alfvénic wave generation in the Sun's atmosphere.