Analyzing data into quantized components

Signals in various applications are often generated by linear combinations of quantized components. The analysis of data into such components is treated here as a matrix analysis problem. We first show that the component alphabet can always be normalized to the levels 0, ..., M-1, without loss of generality. Then we study certain conditions under which the decomposition is possible. In particular, we present an analytical algorithm based on the differences of the observed points and the recursive estimation of the quantized components when the number of unique observed points is sufficiently large.