Multirate Periodic Systems and Constrained Analytic Function Interpolation Problems

IEEE Trans. Signal Process.

Han

2011

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Two-sided diagonal scaling for transfer matrices is formulated. An efficient algorithm is proposed to compute globally optimal solutions using the iterated bi-section and linear matrix inequality (LMI) solver. It is shown that the two-sided scaling of filter bank (FB) frames can be implemented by the adjustment of channel gains and the periodic precoding of source signal, and that the frame-bound-ratio of FB frames can be effectively improved by such scaling. Explicit formulas are established for both uniform and nonuniform FB frames, including detail formulas for discrete Weyl-Heisenberg frames and tree-structured FBs (discrete wavelets). Different examples show the effectiveness of the obtained results.Index Terms-Condition number, diagonal scaling, discrete wavelets, filter banks, frame bound ratio.

Section: Discussionmentioning

confidence: 91%

Optimal Two-Sided Diagonal Scaling for Filter Bank Frames

IEEE Trans. Signal Process.

Han

2011

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“…It is worth noting that our methods apply to frames generated by other non-uniform FBs as long as their polyphase matrix has a statespace realization. The results can also be extended to general multirate systems formulated in [22].…”

Section: Discussionmentioning

confidence: 93%

Bound-ratio minimization of filter bank frames by periodic precoding

2011 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

2011

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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 effectiveness of our results.

“…Hence is a linear shift invariant (LSI) system from 2 (ℂ ) to 2 (ℂ ), and it has a transfer matrix representation [14] ( ) =…”

Section: A Linear Periodically Shift Variant Systems and Blockingmentioning

confidence: 99%

“…Recently, state-space based methods are introduced to various problems arising from the analysis and design of FB frames [11], [12], [13]. The general multirate periodic model described in [14] covers most of the LSPV systems as special cases.…”

Section: Introductionmentioning

confidence: 99%

On shift variance bounds in multi-channel filter banks

Han

2012 IEEE International Symposium on Circuits and Systems

2012

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Shift variance bounds of critically sampled multirate filter banks are usually defined by using eigensystem analysis of the commutator operator. Computational methods are provided for two-channel FIR filter banks by Aach and Fuhr (2009). This paper investigates shift variance bounds in oversampled multi-channel filter banks and derives some general results which include some of Aach and Fuhr (2009) as special cases. Using polyphase representation, numerical methods are provided to compute the shift variance bounds for arbitrary filter banks. Examples are given to demonstrate the effectiveness of the obtained results.