Suppression of limit cycles in the first-order two-dimensional direct form digital filter with a controlled rounding arithmetic

The first-order two-dimensional direct-form digital filter with magnitude truncation is known to be free from limit cycles for a limited range of allowed filter coefficients. In this correspondence, the quantization technique of controlled rounding is used to extend the region of filter coefficients for which suppression of limit cycles can be proved. With controlled rounding a signal is quantized in the direction of a control signal, which is formed by an integer combination of preceding signal values. The absence of limit cycles is proved with a properly chosen Lyapunov function