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This paper presents a new and efficient method to approximate all-pole analog filters by considering magnitude constraints in the frequency domain. A specified tolerance scheme is transformed into a linear programming problem, which can be efficiently solved by available optimization software. Thereby, the use of linear programming enables the designer to compute filter coefficients by optimizing design variables as e.g. the gain ripple in pass band. Furthermore, this approach makes possible to easily find alternative low order filters in a larger solution space, which will lead to a cost reduction in the design flow. Additionally, a modified form of the proposed method can be employed to consider coefficient uncertainties caused by component variations. Examples are provided to validate the benefits of the resulting design method.