Setting the phase-frequency response of digital filters with finite impulse response regardless of the amplitude-frequency response

The article discusses the implementation of a bandpass digital filter with independent adjustment of the phase-frequency response. By adjusting the phase-frequency characteristic we mean changing its angle of inclination, including the inverted form of the phase-frequency characteristic, that is, a negative angle of inclination. This makes it possible to obtain not only a small range of changes in the phase of the output signal in the filter passband, but also different signs of the slope of the phase-frequency characteristic. Carrying out such settings using known methods of implementing digital filters is impossible, since it contradicts physics. The solution to this problem is possible using a two-channel circuit for converting the input signal at multiple frequencies. The problems of adjusting the phase-frequency characteristic of a digital filter, independent of the amplitude-frequency characteristic, arise when designing digital self-oscillating systems. To fulfill the phase balance condition, it is necessary to eliminate ambiguity between frequencies and phase shifts. The range of changes in the phase-frequency characteristics in the passband should be within 2π. These requirements are met for analog filters, however, for digital filters, phase wrap is determined by the order of the filter. This leads to the fact that within the filter's passband, the phase-frequency characteristic zero can occur many times. The article presents a structural and mathematical model of a digital filter with an adjustable phase-frequency response, and its simulation was carried out in the MATLAB - Simulink environment. During the operation of the model, the dependences of the signal at the output of the blocks were obtained. Included in the structure of the model and it is shown that the experimental results do not contradict the mathematical model. The simulation result showed the effectiveness of tuning the phase-frequency response. Examples of setting the slope angle of the phase-frequency characteristic for three cases are shown: a small slope angle of the phase-frequency characteristic, zero equivalent phase-frequency characteristic and inverted (atypical) phase-frequency characteristic. Based on the results of the work, conclusions were drawn.