This paper reports on a theoretical investigation into some of the properties of ensemble averaged electromyographic profiles (EAEPs) which are frequently applied in gait analysis. The study treats the quantification of the surface EMG signal by means of a linear envelope detector as an estimation problem. The surface EMG signal obtained in gait analysis is modelled as an amplitude modulated Gaussian random signal with a limited bandwidth, and the smoothed rectified EMG (SRE) signal at a given instant is interpreted as an estimate of the local standard deviation over a short time-averaging interval. An equivalent impulse response for the linear envelope detector's lowpass filter is introduced. This allows the prediction of the detector's response to the modulated EMG signal. The results show that stochastic estimation errors may contribute considerably to the observed variability in EAEPs. They also explain how these errors depend on the spectral characteristics of the EMG signal, the design of the lowpass filter in the linear envelope detector and on the time course of a muscle's myoelectric activity.