Nonlinear processes in digital filters with quantization and overflow

Processes in digital filters are analyzed with consideration for the effects of quantization at an arbitrary number of digits in the representation of numbers and overflow under periodic external influences. An analysis technique based on representation of stationary oscillations as an invariant set of nonlinear discrete point mappings is used. The spectral composition of the system response and nonlinear distortions of signals with an arbitrary period are calculated with the use of classical and modernized discrete Fourier transforms. The results of calculations of processes in digital bandpass Butterworth and Chebyshev filters are presented. The dependences of the nonlinear distortion coefficient on the encoding type, the number of digits in the representation of numbers, and the order of the digital filter are demonstrated. The influence of the number of digits on frequency responses of filters is determined.