The possibility of quantizing the coefficients of a digital filter in the concept of dynamic mathematical
 programming, as a dynamic process of step-by-step quantization of coefficients with their discrete optimization at
 each step according to the objective function, common to the entire quantization process, is considered. Dynamic
 quantization can significantly reduce the functional error when implementing the required characteristics of a lowbit digital filter in comparison with classical quantization. An algorithm is presented for step-by-step dynamic
 quantization using integer nonlinear programming methods, taking into account the specified signal scaling and the
 radius of the poles of the filter transfer function. The effectiveness of this approach is illustrated by dynamically
 quantizing the coefficients of a cascaded high-order IIR bandpass filter with a minimum bit depth to represent integer
 coefficients. A comparative analysis of functional quantization errors is carried out, as well as a test of the quantized
 filter performance on test and real signals.