The instantaneous amplitude (magnitude) and instantaneous frequency (phase derivative) waveforms of analytic vector representations of speech, models of speech and sub-bands of speech are generated and analysed. Important characteristics of the instantaneous parameter waveforms are identified. These are related to attributes of vector loci and. the spectral and zero structure of the associated real and analytic signals. Real time generation and display of the analytic vector and its parameters is achieved and associated difficulties identified. The problem of reconstruction of speech from its instantaneous parameters and from modified instantaneous parameters is addressed. Resulting distortions are classified and an application to low bit rate speech transmission investigated.