Signal channelization enables efficient frequency domain processing and is a mainstay of astronomical signal processing, but applications that require high time resolution necessitate reconstruction of the original wide band signal. In a previous paper, a near-perfect method of reconstructing a time-limited input signal from the output of an oversampled polyphase filterbank (PFB) was described. Here, we consider the case where continuous signals are processed. We show that the most simplistic approach, which utilizes non-overlapping windows and a fast Fourier transform (FFT) channelizer, introduces large errors whose magnitude can equal the signal. The ringing introduced by truncation at the end of a block, combined with the cyclic nature of FFTs, leads to errors that are concentrated at block boundaries. These localized errors can be heavily suppressed by utilizing overlapping windows and nearly completely eliminated by apodizing the data blocks with a Tukey window. After these improvements, the much smaller residual error is concentrated at the PFB channel boundaries and is due to adjacent channels having different gain slopes at the channel boundary. Increasing the channel passband equalizes the gain slope at the channel boundary, and the error is reduced further. With these changes, errors as low as −100[Formula: see text]dB are achieved, and the method of reconstructing the channelized data meets the stringent signal purity requirement for astronomical applications such as radio pulsar timing.