Optimal finite impulse response (FIR) error feedback filters for noise shaping in Ã?â?Ã?£ modulators are designed by using\nweighting functions based on the system norms. We minimize the weighted norms of the quantization error in the\noutput of a Ã?â?Ã?£ modulator, which corresponds to the minimization of the system norm. Three norms, the H2 system\nnorm, the HâË?ž system norm, and the l1 norm of the impulse response of the system, are adopted. The optimization\nproblem for three types of FIR filters are evaluated by using linear matrix inequalities (LMIs) and then solved\nnumerically via semi-definite programming. Design examples are provided to demonstrate the effectiveness of our\nproposed methods.
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