A popular model of the processing of amplitude modulation (AM) [Viemeister, J. Acoust. Soc. Am. 66, 1364--1380 (1979)] consists of a bandpass filter, a rectifying nonlinearity, a low-pass filter, and a decision device. The low-pass filtering (or integration) stage was intended to simulate the temporal resolution limit by attenuating rapid changes in the envelope of the signal. Fleischer [Acustica 47, 155--163 (1981)] developed a model describing the influence of the inherent fluctuations within a noise carrier on the detectability of added modulation. The modulation spectrum was weighted by a certain factor which also essentially represented a low-pass characteristic. In a recent modeling approach [Dau et al., submitted to J. Acoust. Soc. Am. (1997)], a modulation filterbank replaced the low-pass filter, to analyze the envelope fluctuations of the stimuli in each peripheral auditory filter. The inclusion of a modulation filterbank was motivated by results from several studies on modulation masking which provided evidence for frequency selectivity in the modulation-frequency domain. In addition, the role of peripheral filtering for the processing of amplitude modulation, the envelope statistics, and the spectral distribution of modulation power in the modulation spectrum are discussed.