Based on the compact support property of popular multi-channel filter banks, a low-memory implementation of generic tree-structured filter banks (TSFBs), called the stripe-based tree-structured filter bank (SBFB), is presented by utilizing the first-in first-out (FIFO) buffer technique. The SBFB has two advantages: (1) It produces exactly the same sub-band coefficients as the conventional global implementation of TSFB does, while the memory budget is unrelated to the image height and only dependent on the image width and the TSFB adopted. As a result, the memory budget of SBFB is only a fraction of that of the global implementation; (2) It generates integral parent-children trees (PCTs), which are completely contained in its buffers. The SBFB lends itself to PCT-based coders in that no intermediate buffering is needed between the SBFB and the coder. By analyzing the dataflow of different levels of TSFB, the relation between the samples and the sub-band coefficients is also attained, by which the correctness of the SBFB is strictly proved.