On the Robustness of Filter Bank Frame to Quantization and Erasures

This paper studies the robustness of filter bank (FB) frame in l² (Zopf) to quantization and erasures from the perspective of both frame and FB theory. It is shown that the equal-norm property, imposed frequently in previous papers, is not necessary for optimization of frames under certain conditions and not desirable from the viewpoint of designing FB frames. We introduce a novel notion, named frame energy, which actually dictates the quantization performance of FB frames. Then, the erasure effects on the structures and quantization performance of FB frames are investigated. The design freedom obtained from removing the equal-norm property is explained and illustrated with examples.