Marginal Probability Density Function of Granular Quantization Error in Uniform Quantizers

In this correspondence, the authors analyze the validity of the uniform model for the marginal probability density function (pdf) of granular quantization error (QE) in a uniform quantizer, subjected to random input signals. Two theorems are proved, which show that the knowledge of the average of such error as a function of input signal average, suffices for the determination of the quantization error pdf (QEpdf). This result is employed to derive simple expressions for the QEpdf in the case of random inputs with uniform, sinusoidal, or Gaussian distributions.