Two-channel digital and hybrid analog/digital multirate filter banks with very low-complexity analysis or synthesis filters

Multirate filter banks make use of analysis and synthesis filter banks. This paper introduces two-channel digital and hybrid analog/digital multirate filter banks where either the analysis or synthesis filters have a very low complexity. Such filter banks find application, for example, in high-speed analog-to digital converters where it is essential to minimize the complexity of the discrete-time or analog filters. The proposed digital filter banks are approximately perfect reconstruction (PR) filter banks, whereas the hybrid analog/digital filter banks can be chosen to be either approximately PR or approximately perfect magnitude reconstruction filter banks. The design is performed by first optimizing the digital or analog analysis filters and then, with the analysis filters fixed, optimizing the digital synthesis filters. This design procedure makes it possible to obtain analysis filters of very low order and complexity. The overall complexity is also low. Further, the proposed filter banks are, in all cases, very easy to design by making use of well-known and reliable optimization techniques; in particular, as small distortion and aliasing as desired are readily obtained because they are controlled in a linear programming problem. Several design examples are included, illustrating the properties of the proposed filter banks.