Spectrum of a nonlinearly quantised sinusoid (ADC)

A simple approach is proposed for obtaining analytical expressions for the harmonic distortion resulting from nonlinear quantisation of a single sinusoid using an actual analogue-digital convertor exhibiting nonlinearity error. The actual-digital converter characteristic is split into two nonlinear characteristics; the first represents the nonlinearity error and the second represents the quantisation. Whereas the nonlinearity error characteristics is modelled by a third-order polynomial, the quantisation is modelled by an ideal staircase. Series expressions are obtained for the output spectra of an actual analogue-digital convertor excited by a single sinusoid. Special cases are considered where the series expressions can be reduced to simple analytical expressions. Also, the feasibility of minimising the total harmonic distortion is explored.