Bound-ratio minimization of filter bank frames by periodic precoding

Frame (upper and lower) bound ratio is a key factor of numerical stability of frame systems. While tight frames, of which the minimal ratio 1 is achieved, are much preferred in many practical situations, they may not be easily (even impossible) designed due to other criteria (for example, good subband frequency shape). In these situations, we may find alternative methods for improving the frame-bound-ratio. This paper studies the minimization of frame-bound-ratio for filter bank frames by using periodic precoding. A convex optimization based algorithm is proposed. Examples show the effective ness of our results.