Some problems associated with sub-band coding of images are investigated. The filtering operations needed for splitting an input into different frequency bands, as well as their reconstruction, require an extension beyond the length of the finite signal. If not properly made, the necessary signal extension can yield distortion of the reconstructed signal, and it may complicate the compression of high-pass frequency bands. Five different methods of signal extensions have been investigated for sub-band coding. It turns out that extending the signal so that continuity is maintained may be a sufficient remedy, as shown in an image coding example.