Third-Order Intermodulation Due to Quantization

When an input consisting of a strong signal and a weak signal is handled digitally, the resulting quantization introduces not only noise and distortion of the stronger signal (which have been thoroughly studied elsewhere) but also intermodulation between the two. Third-order intermodulation is the principal source of spurious inband signals, and it is important, therefore, to determine its strength in comparison with that of the true weak-signal output, which is of the same order of magnitude. The assumption that the weaker signal's amplitude
a
is very much smaller than the quantization step size permits a relatively simple analysis by means of two different approaches. Both of them lead to a finite series for the amplitude
c_{2}a
of the intermodulation. This series is easily evaluated numerically, but simple approximations obtained by truncation of Euler's summation formula show the behavior of c
2
more clearly as a function of the amplitude of the stronger input and will be found adequate for most applications.