Envelope modelling of impulse response functions of systems having a high modal density

The description of the transmission of a transient excitation through a complicated (but linear) channel is expressible as a convolution (by a ´complicated´ system we mean one whose frequency response exhibits a high modal density). The basic convolution expression (or its frequency domain equivalent) is often not convenient for investigation of a particular class of processes; namely, when an ensemble of excitations drives a system in a variety of different (though similar) ways then it is desirable to quantify some form of ´average behaviour´ of the system and response, with the aim being to provide characterisations that reflect the main features of the signals and not the detailed temporal behaviour. In this paper we present just such an analysis which describes the input, response and system impulse response in terms of the envelope of each signal in frequency bands using the concept of the analytic signal.