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• ANALYSIS OF STABILITY AND FEATURES OF PRACTICAL IMPLEMENTATION OF HOGENAUER FILTERS AS RECURSIVE DIGITAL FILTERS WITH FINITE IMPULSE RESPONSE

  I.Е. Moiseenko , S. P. Tarasov , I.I. Turulin

  37-46

  2025-10-01

  Abstract ▼

  The article considers the issues of stability of cascade integrator-comb (CIC) filters used in digital signal processing, including decimation and interpolation. A brief review of modern publications on the architectural optimization of CIC filters is given. The main attention is paid to increasing the stability of filters to the overflow of the bit grid, analyzing their stability and the method of synthesis of recursive FIR filters (filters with a finite impulse response). For a better understanding of the nature of the stability of CIC filters, the paper presents mathematical calculations illustrating the features of the accumulation of the constant component for various block configurations. A change in the structure of the CIC filter is proposed, consisting in the permutation of the integrator and comb filter blocks. It is proved that such a change prevents the accumulation of the constant component of the signal in the integrators and, therefore, eliminates the overflow of the bit grid due to the accumulation of the constant component in the integrator. This approach is based on the property of linear filters, according to which changing the order of inclusion does not affect the transfer function. amplitude-frequency characteristic, but in the case of digital implementations it allows to significantly reduce the probability of overflow. The possibilities of hardware and software implementation of such structures are considered from the point of view of minimizing the loss of accuracy and increasing the reliability of digital signal processing systems. It is proposed to use integers or numbers with a fixed point to eliminate the accumulation of quantization errors. In addition, a program in Python was developed that implements a CIC filter taking into account the stability of the constant component in the input signal and the accurate execution of operations. The obtained results are compared with modern approaches presented in scientific research in recent years. The proposed solutions can be useful in developing digital filters for systems with limited computing resources and increased stability requirements.

• METHODOLOGY OF REALIZATION ON PLIS OF A CONTROLLED RECURSIVE FILTER WITH A FINITE IMPULSE RESPONSE IN THE FORM OF AN APPROXIMATION OF THE HANN WINDOW

  D.I. Bakshun, S.P. Tarasov, I. I. Turulin

  2025-01-30

  Abstract ▼

  The paper considers the methodology of realization of recursive filter with finite impulse response
  (FIR) in the form of Hahn window with the possibility of controlling the duration (in counts or cycles) of
  FIR, including in the process of filtering, based on simultaneous sequential compensation of samples from
  the recursive part. A brief review of the existing solution for controlling the duration of a rectangular
  pulse characteristic is performed and the methods of realization of impulse response of more complex
  shape on the example of a Hahn window are proposed. The method proposed by the authors allows to
  achieve stability of the filter when the duration of the impulse characteristic changes in time. The structure
  of the module for realization of the filter on the basis of Field-Programmable Gate Array (FPGA) is developed.
  The recursive filter structure considered in this paper has significantly lower computational
  complexity compared to the classical FIR filter structure, and it can be used in embedded systems with
  limited computational resources. The lower computational complexity is achieved by using the function
  approximating the Hahn window, which is a third-degree polynomial, as the FIR. Filtering is accomplished
  by using two independent filters, one tuned to the duration of the FIR before its change and the
  other tuned to the duration of the FIR afterwards with the result summarized. This approach is based on
  the principle of linearity of the system, which allows combining the output signals of the filters without
  losing their properties. The control of the delay duration is performed based on the ability of the dualported
  RAM memory to simultaneously write and read. When changing the FIR duration, the calculation
  of filter coefficients is performed during filtering, thus eliminating interruptions between the output signal
  sections before and after changing the FIR duration. There is a protection against entering a new parameter
  of the FIR duration before the transient compensation due to the previous change of the FIR duration
  is completed. After the compensation procedure is completed, the filter tuned to the FIR duration before it
  was changed is terminated.