Abstract: A signal processing method and apparatus including a digital finite impulse response filter wherein the error caused by slow asymptotic convergence of the filter's adaptive coefficients is reduced. A first input signal is provided to an adaptive FIR filter including a coefficient calculator, finite impulse response FIR filter and a summation device. The filter also receives a second input signal, which may, for example, be the echo of the first input signal. The first input signal and the second input signal have a first bandwidth. The adaptive FIR filter then provides an output signal to a filter, which then filters the output signal to a second bandwidth which is less than the first bandwidth. The processed signal will have less error caused by the slow asymptotic convergence of the filter than previously possible because the error-concentrated frequency components near the band edge of the first frequency band have been filtered or removed.