In this paper, we present a novel algorithm called Suppression of Slowly-varying components and the Falling edge of the power envelope (SSF) to enhance spectral features for robust speech recognition, especially in reverberant environments. This algorithm is motivated by the precedence effect and by the modulation frequency characteristics of the human auditory system. We describe two slightly different types of processing that differ in whether or not the falling edges of power trajectories are suppressed using a lowpassed power envelope signal. The SSF algorithms can be implemented for on-line processing. Speech recognition results show that this algorithm provides especially good robustness in reverberant environments.