The effect of noise on adaptive envelope-constrained filters

The performance of the envelope-constrained filters designed by the newly developed adaptive algorithms may deteriorate when the input signal is contaminated by noise. The average window with a growing window size, and the exponentially weighted average window are presented. It is shown that the noise-induced bias in the augmented cost function will be reduced because applying such an averaging scheme helps increase values of the signal-to-noise ratio at the filter input channel. With this, the noise effect on the adaptive envelope-constrained filters can be depressed. Simulation results are given to illustrate the improved performance of the adaptive envelope-constrained filters designed in conjunction with the average window.