Frequency channelization is a fundamental signal processing operation employed across various domains, including communications and radio astronomy. The polyphase filterbank (PFB) represents an efficient and versatile means of channelization. When strict constraints are placed on the allowable spectral leakage between neighboring channels, an oversampled PFB design is advantageous. A helpful consequence of the oversampling is that inversion of the PFB to recover high temporal resolution is simplified and can be accomplished accurately using Fourier transforms. We describe this inversion approach and identify key design considerations. We examine the residual error and spectral/temporal leakage behavior when a channelizer and its corresponding inverter are cascaded, concluding that near-perfect reconstruction can be approached with appropriate selection of PFB and inverter design parameters.