Structurally random matrices (SRMs) have been proposed as a practical alternative to fully random matrices (FRMs) for generating compressive sensing measurements. If the compressive measurements are transmitted over a communication channel, they need to be efficiently quantized and coded and hence knowledge of the measurements’ statistics reequired. In this paper we study the statistical distribution of compressive measurements generated by various types of SRMs (and FRMs), give conditions for asymptotic normality and point out the implications for the measurements’ quantization and coding. Simulations on real-world video signals confirm the theoretical findings and show that the signal randomization of SRMs yields a dramatic improvement in quantization properties.