Implicit decimation for FIR systems and its application to acoustic echo cancellation

This paper presents a filter structure which performs implicit decimation of the impulse response. As a result, the number of required operations is reduced or, equivalently, the impulse response length of the filter can be increased. Analysis in the frequency domain shows that this implicit decimation can be applied to systems that exhibit low-pass characteristics or have a smooth transfer function at high frequencies. Such behaviour can be assumed for many technical systems. For the determination of the optimal coefficients many well known algorithms for FIR systems can be used after a slight modification of the signal vector. The performance of implicit decimation is demonstrated for acoustic echo cancellation. Comparison with different algorithms shows that implicit decimation outperforms conventional FIR filtering.