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

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.