  In this paper, we examine the optimal quantization of signals for system
identification. We deal with memoryless quantization for the output signals and
derive the optimal quantization schemes. The objective functions are the errors
of least squares parameter estimation subject to a constraint on the number of
subsections of the quantized signals or the expectation of the optimal code
length for either high or low resolution. In the high-resolution case, the
optimal quantizer is found by solving Euler-Lagrange's equations and the
solutions are simple functions of the probability densities of the regressor
vector. In order to clarify the minute structure of the quantization, the
optimal quantizer in the low resolution case is found by solving recursively a
minimization of a one-dimensional rational function. The solution has the
property that it is coarse near the origin of its input and becomes dense away
from the origin in the usual situation. Finally the required quantity of data
to decrease the total parameter estimation error, caused by quantization and
noise, is discussed.
