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Two new design methods for infinite-duration impulse-response (IIR) multirate digital filters are introduced, and a state-variable implementation is given. One method is an extension of the impulse-invariant method and results in the direct synthesis of a multi-rate filter which realizes in discrete time the response of a continuous time circuit. The second method employs linear programming (LP) to optimize the frequency domain response. For finite-length impulse response (FIR) multirate filters an efficient fast Fourier transform (FFT) implementation is presented.
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Meyer et al. (1976) studied this question.
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