This paper investigates waveform interpolation (WI) applied low bit rate wideband speech coding. An analysis of the evolutionary behaviour of wideband characteristic waveforms (CW) shows that direct application of the classical WI algorithm may not be appropriate for wideband speech. We propose a modification whereby CW quantisation is performed using classical WI decomposition for the low frequency region and noise modelling for the high frequency region. Wideband WI coders incorporating this modification and operating at 4 kbit/s and 6 kbit/s are described. Subjective testing of these coders shows that WI is a promising approach to low bit rate wideband speech compression.