tree-structured decomposition that leads to subbands with wedge-shaped frequency partition (see Figure). The original construction of the DFB involves modulating the input signal and using diamond-shaped filters. Moreover, in order to obtain the desired frequency partition, a complicated tree expanding rule has to be followed. As a result, the frequency regions for the resulting subbands do not follow a simple ordering as shown in Figure 9 based on the channel indices. The first advantage of DFB is that not only it is not a redundant transform but also it offers perfect reconstruction. Another advantage of DFB is its directional-selectivity and efficient structure. This advantage makes DFB an appropriate approach for many signal and image processing usage. (e.g., Laplacian pyramid, constructed the contourlets, sparse image representation, medical imaging, etc.). Directional Filter Banks can be developed to higher dimensions. It can be use in 3-D to achieve the frequency sectioning. Filter-bank transceiver Filter banks are important elements for the physical layer in wideband wireless communication, where the problem is efficient base-band processing of multiple channels. A filter-bank-based transceiver architecture eliminates the scalability and efficiency issues observed by previous schemes in case of non-contiguous channels. Appropriate filter design is necessary to reduce performance degradation caused by the filter bank. In order to obtain universally applicable designs, mild assumptions can be made about waveform format, channel statistics and the coding/decoding scheme. Both heuristic and optimal design methodologies can be used, and excellent performance is possible with low complexity as long as the transceiver operates with a reasonably large oversampling factor. A practical application is OFDM transmission, where they provide very good performance with small additional complexity. Notes References Further reading Digital signal processing Linear filters Wavelets