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Allpass transformed filter banks provide a nonuniform frequency resolution and can be used in mobile speech processing systems, e.g., cellular phones or digital hearing aids. The nominal design of such an allpass transformed analysis-synthesis filter bank (AS FB) with near perfect reconstruction (NPR) is achieved by numerical optimization of finite-impulse response (FIR) equalizers in each subchannel. The underlying nominal optimization problem is an equality constrained leasts-quares problem. In a robust design, we take into account coefficient uncertainty in a possible implementation of such a filter bank. We will describe this uncertainty by the choice of two simple set-based worst-case uncertainty models, namely a norm bound error model and a coefficient bound error model. When including these error models, both robust designs can be recast as second-order cone programs (SOCP) and solved efficiently by standard numerical optimization methods. Furthermore, we will provide design examples to show that both robust designs maintain a good overall performance with respect to NPR while offering less sensitivity to quantization errors.