  Many modern distributed real-time signal sensing/monitoring systems require
quantization for efficient signal representation. These distributed sensors
often have inherent computational and energy limitations. Motivated by this
concern, we propose a novel quantization scheme called approximate Lloyd-Max
that is nearly-optimal. Assuming a continuous and finite support probability
distribution of the source, we show that our quantizer converges to the
classical Lloyd-Max quantizer with increasing bitrate. We also show that our
approximate Lloyd-Max quantizer converges exponentially fast with the number of
iterations. The proposed quantizer is modified to account for a relatively new
quantization model which has envelope constraints, termed as the envelope
quantizer. With suitable modifications we show optimality and convergence
properties for the equivalent approximate envelope quantizer. We illustrate our
results using extensive simulations for different finite support source
distributions.
