Improving frame-bound-ratio for frames generated by oversampled filter banks

Abstract

This paper presents a simple method to improve the frame-bounds-ratio of perfect reconstruction (PR) oversampled filter banks (FBs) by adjusting the gain of each subband filter. For a given analysis PRFB, a finite convex optimization algorithm is presented to redesign the subband gains such that the frame-bounds-ratio of the FB is minimized. The algorithm also provides an effective way to compute the frame bounds. Examples show the effectiveness of the presented method.

Bound Ratio Minimization of Filter Bank Frames

“…This paper investigates the problem of frame bound ratio minimization of oversampled PRFBs with prespecified subband channel peformance. It is partially based on our recent conference paper [14] and extends our result in [15] which is on reliable computation of the frame bound ratio of FBs. Our investigation is motivated by the fact that many practical FBs in operation were designed to meet subband specifications without fully considering the frame bound ratio as a global performance index.…”

“…It is easy to verify that the left-hand side of inequality (36) is the same as the left-hand side of (13). Similarly, it can be shown that (35) holds if and only if there exists such that (14) holds. This completes the proof.…”

“…By Lemma 4 and Theorem 1, maximizing for is equivalent to minimizing the frame bound ratio of , and the minimization can be achieved by the optimization (12) subject to (13) and (14). Let and be the solution to the optimization (12) subject to (13) and (14). Then, as shown in the proof of Lemma 4, is the optimal solution with the upper frame bound and the maximized lower frame bound .…”

“…Thus, maximizing , the lower frame bound of , subject to the constraint (29) will minimize while keeping the output variance of bounded. By Lemma 4 and Theorem 1, maximizing for is equivalent to minimizing the frame bound ratio of , and the minimization can be achieved by the optimization (12) subject to (13) and (14). Let and be the solution to the optimization (12) subject to (13) and (14).…”