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• METHOD AND ALGORITHM FOR SYNTHESIS OF CONTROLLED CHEBYSHEV DIGITAL FILTERS OF THE FIRST KIND OF LOW FREQUENCIES BASED ON THE BILINEAR TRANSFORMATION METHOD

  I.I. Turulin, S.M. Hussein

  2022-11-01

  Abstract ▼

  The article presents a technique for the synthesis of controlled digital recursive Chebyshev lowpass
  filters of the first kind with an infinite impulse response. The frequency response of such filters has
  ripples in the passband and is as flat as possible in the stopband. Controllability is understood as an
  explicit dependence of the filter coefficients on the cutoff frequency. The technique is based on the bilinear
  transformation of the transfer function of the analog low-pass filter prototype and the frequency
  transformation of the amplitude-frequency characteristics of the obtained digital filter. The main idea ofthe technique is that for an analog prototype filter with a cutoff frequency of 1 rad/s, the parameters of
  the transfer function of biquadratic or bilinear links, which have the dimension of frequency, will be
  numerically equal to the correction factors for similar parameters of a controlled filter with an arbitrary
  cutoff frequency. As an example, the synthesis of a digital Chebyshev filter of the first kind of the fifth
  order is considered. In this article, the transfer function of an arbitrary order filter is represented as a
  cascade connection of II order links if the filter is of an even order. In the case of an odd order greater
  than one, one cascaded link of the first order is added. Despite the relative simplicity of the frequency
  conversion, in its practical use for digital filters synthesized using computer-aided design of digital filters
  (or using reference books containing calculated prototype low-pass filters for various approximations
  of the frequency response of an ideal low-pass filter), a series arises non-trivial specific moments
  that complicate the engineering use of this method of synthesizing controlled digital filters. Therefore, in
  addition to the technique, a step-by-step algorithm has been developed that allows one to synthesize a
  filter without knowing these moments. The algorithm is implemented in the Mathcad environment; as
  an example, a digital recursive Chebyshev filter of the 1st kind of the 5th order is calculated.
  The example shows the calculated coefficients of a digital controlled low-pass filter, which explicitly
  depend on the cutoff frequency, the amplitude-frequency characteristics of this filter and its lowfrequency
  prototype converted into a filter with the same cutoff frequency, the amplitude-frequency
  characteristics are given in the same coordinates. Due to the good formalization of the algorithm, the
  latter is suitable for the implementation of computer-aided design systems for controlled digital
  Chebyshev low-pass filters of the first kind.

• REDUCTION APPROACH OF TRANSIENT PROCESS OVERSHOOT IN CONTROLLED TUNABLE LOW PASS DIGITAL FILTER

  Al-Karawi Hussein Shakor Mogheer, I.I. Turulin

  2022-08-09

  Abstract ▼

  Digital signal processing is widely used in modern technology, including robotics, medical
  technology, etc. Thus, the controlled digital filters are used to eliminate the constant component of
  the output signal at the output of an analog-to-digital converter. This also reduces the low-frequency
  interference level spread out on the frequency axis to the left of the lower boundary of the signal
  spectrum. In actual situations, signals are subjected to a variety of disruptions and noises; however,
  applying a filter may suppress these noises and produce a clean signal. Controllability means the
  explicit dependence of the filter coefficients on the cutoff frequency. A transient occurrence can arise
  in a digital filter, which is indicated in the overshoot of the signal. A change in the cutoff frequency
  during filtering operation could cause this transient event. In this report, a Butterworth LPF filter is
  used to offer a compensation strategy for reducing this overshoot. A transient is an overshoot (drive)
  in the result timing chart. This drive is an after effect of the adjustment of the coefficients (boundaries)
  of the filter during filtering (this is classified "on-the-fly tuning"). By using the MATLAB program,
  the transient process resulting from the restructuring of the filter was investigated and the
  formulas were checked compensation of this transient process. It was found that the application of
  such compensation reduced the negative effects of the transition process. This decrease depends on
  the order of the filter, the adjustment coefficient (the ratio of cut frequencies before and after adjustment)
  and the moment of adjustment (for the periodic signal).

• ANALYSIS OF MATLAB SYSTEM APPLICABILITY FOR SYNTHESIS OF CONTROLLED BUTTERWORTH DIGITAL RECURSIVE IIR FILTERS

  Hussein Sh. Mogheer, I. I. Turulin

  2021-08-11

  Abstract ▼

  A number of digital signal processing applications use controlled IIR digital recursive filters.
  The word " controlled " refers to filters whose structure ratios clearly depend on the cut rate or
  boundary frequencies. Controlled IIR filters can be synthesized using a variety of tools to compute
  traditional, uncontrolled IIR filters. The article dealt with the synthesis uncontrolled IIR filters and
  analyzed the suitability of the presentation of the results of synthesis for the construction of controlled
  IIR filters. The design techniques based on MATLAB (2021a) and the fundamental concepts of IIRButterworth
  digital filters were described and explained. The composited signal was processed by the
  analyzed filter to find whether it met the filtering progress criteria. To check the calculated filters, the
  Simulink prototype was used, as well as FDA tool of signal processing toolbox. Based on the results
  obtained, a conclusion was made about the applicability of the MAT LAB (2021a) system for the
  synthesis of controlled digital recursive IIR-Butterworth filters. The analyzed technique was more
  efficient, faster, decreased the tasks and found the results are satisfying.