Fourier analysis and synthesis for a mildly non-linear quantizer

We introduce and analyze a method for stabilizing test parameters and estimating the non-linearity of mildly non-linear quantizers by Fourier analysis of the quantizer's output to sinusoidal input signals. Stabilization for the combined effects of the rounding operation of the quantizer and the variations in offset and amplitude of the applied sinusoid is achieved by a deterministic form of subtractive dithering, called wobbling. It thus appears that one can retrieve low-to-medium degree non-linearities whose contribution to the quantizer's distortion in the relevant frequency range is of the same order as or well below the distortion due to rounding before wobbling. For the analysis of the method a thorough investigation of the spectra of sampled, quantized sinusoids (wobbled or not) has to be made. As such we complete and extend existing results in the literature of spectra of this type. The method is potentially useful for estimating the integral non-linearity of AD-converters.