We study the design of synthesis filters in noisy filter bank systems using an H^∞ estimation point of view. TheudH^∞ approach is most promising in situations where theudstatistical properties of the disturbances (arising from quantization, compression, etc.) in each subband of the filter bank are unknown, or are too difficult to model and analyze. For arbitrary analysis polyphase matrices, standard state-space H∞ techniques can beudemployed to obtain numerical solutions. When the synthesis filters are restricted to being FIR, as is often the case in practice, the design can be cast as a finite-dimensional semi-definite program. In this case, we can effectively exploit the inherent non-uniqueness of theudH∞ solution to optimize for an additional averageudperformance and thus obtain mixed H^2/H^∞udoptimal FIR synthesis filters.
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机译：我们使用H ^∞估计的观点来研究噪声滤波器组系统中的合成滤波器的设计。在滤波器组的每个子带中的干扰（由量化，压缩等引起）的统计性质未知，或者难以建模和分析的情况下， udH ^∞方法最有前途。对于任意分析的多相矩阵，可以采用标准状态空间H∞技术获得数值解。当将合成滤波器限制为FIR（在实践中通常是这种情况）时，可以将设计转换为有限维半定程序。在这种情况下，我们可以有效地利用udH∞解的固有非唯一性来优化其平均性能，从而获得混合的H ^ 2 / H ^∞最佳FIR合成滤波器。
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