In this paper, we describe a simple gradient algorithm for adapting the phase response of an FIR filter whose magnitude response is already specified. The algorithm is an extension of a previously-developed gradient adaptive algorithm for allpass filtering. The algorithm directly adjusts the impulse response of the FIR filter using input and desired response signals in a simple manner without the need for frequency-domain processing or coefficient monitoring. A stationary point analysis of the algorithm verifies its desirable estimation capabilities. Simulations confirm the capability of the algorithm in a filter modeling task.
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