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• FORMATION OF THE IMPULSE RESPONSE OF A RECURSIVE LOW-PASS FILTER WITH FINITE IMPULSE RESPONSE AS A SUM OF QUASI-HARMONICS OF A TRUNCATED FOURIER SERIES

  D.I. Bakshun , I.I. Turulin

  221-228

  2025-12-30

  Abstract ▼

  The problem of reducing the number of arithmetic operations in digital filtering algorithms is highly relevant, as it directly impacts power consumption, processing speed, and hardware costs. Under strict power efficiency requirements for mobile and embedded systems, minimizing multiplication and addition operations becomes a critical design factor. This paper presents a method for implementing a recursive filter with a finite impulse response (FIR) based on a truncated sinc function smoothed by a window (weighting function), represented as a sum of quasi-harmonic functions. These quasi-harmonic functions with different frequencies are polynomials of degree r. The study adopts a second-degree polynomial as a baseline and proposes a numerical method for increasing the polynomial order to improve the accuracy of the approximation. Accuracy analysis demonstrates that using 4th- and 6th-order polynomials achieves an approximation error of less than 1%. The coefficients of the non-recursive part of the filter are computed via inverse finite differences of the original FIR impulse response. These coefficients are integers whose values depend on the number of samples (length) of the half-period of the quasi-sinusoidal function, simplifying the implementation of such a recursive FIR (RFIR) filter on a field-programmable gate array (FPGA). Numerical analysis of finite differences for each quasi-sinusoid revealed that quadratic approximation requires only 16 samples but results in relatively high side-lobe levels (–30 dB). Switching to 4th-order approximation increases the number of non-zero coefficients to 20 and significantly reduces
  (by 13 dB) the stopband magnitude of the frequency response, reaching –43 dB.

• 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.

• COMPARATIVE ANALYSIS OF TWO FILTERING METHODS TO ELIMINATE NOISE IN AN IMAGE OF DIFFERENT DEGREES OF NOISE

  K.O. Sever, I.I. Turulin, D.A. Guzhva

  2021-08-11

  Abstract ▼

  In modern photography and video technology, any image in the process of its creation is
  distorted by various types of noise. There are various types of noise, but in practice, impulsive and
  Gaussian noise models are the most common. Attenuation of the effect of noise is achieved by filtering.
  At the moment, there is no universal filter that suppresses noise data at various intens ities
  of distortion. Therefore, an important aspect is to determine the field of application of each
  type of filter when suppressing noise in the image and creating a filter, consisting of a combination
  of different filtering methods for optimal image cleaning. The article presents a comparative
  analysis of median filtering and Wiener filtering to eliminate impulse and Gaussian noise in
  the image with different degrees of noise. For modeling, we used one image, separately distorted
  by impulse and separately by Gaussian noise with pixel distortion probabilities from 1% to
  99% inclusive. Filtration was performed with windows equal to 3x3 and 5x5. As a result, we
  obtained numerical estimates of the image filtering quality based on the peak signal-to-noise
  ratio (PSNR). On the basis of the data obtained, the application of the investigated filters, their
  modifications, advantages and disadvantages were analyzed, as well as recommendations for
  their use were given. As a result of a comparative analysis of the studied types of filtering for
  noisy images, it was found that the median filter with a 3x3 window copes better with image
  cleaning from low-intensity impulse noise and with a 5x5 window - with image cleaning with an
  average noise intensity. Also, the median filter does a better job of filtering out Waussian noise
  at its medium and high rms deviations. The Wiener filter with 3x3 and 5x5 windows better fi lters
  Gaussian noise at small values of its root-mean-square deviation. Also, the Wiener filter
  copes better with impulse noise with relatively high noise power.

• 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.

• ANALYSIS OF CERTAIN WEIGHT FUNCTIONS (WINDOWS) AND THEIR APPROXIMATIONS FOR IMPLEMENTATION OF CONTROLLED RECURSIVE LOW-PASS FILTERS WITH A FINITE IMPULSE RESPONSE ON THEIR BASIS

  T.V. Shushkevich , А.А. Morozov, I. I. Turulin

  2021-11-14

  Abstract ▼

  There are various types of weighting functions, the so-called windows in digital signal processing,
  such as rectangular (Dirichlet window), triangular (Bartlett window), Vallee-Poussin window,
  Kaiser-Bessel window, Barsilon-Temesh window, Hann, Bohman, Blackman, Gauss (Weierstrass),
  Dolph - Chebyshev, Hamming windows and many others and ideal characteristics of standard filters
  such as low-pass, high-pass, bandpass filters. The purpose of this review article is to determine the most
  suitable weighting function for implementation on its basis of a controlled recursive low-pass filter with
  a finite impulse response. This article presents an analysis of only some of the above windows and their
  approximations, namely the Dolph - Chebyshev window, the Gauss (Weierstrass) window and the
  Hamming window. In addition to the analysis, the synthesis of recursive filters with a finite impulse
  response for weighting data based on the selected windows and their approximations was considered.
  The method of synthesis of Dolph-Chebyshev windows is considered. The implementation of the Gauss
  (Weierstrass) window is considered. Methods for approximating the Hamming window and methods
  and several algorithms for developing filters with FIR in the form of this window are considered. The
  estimation of parameters dependencies some quick window of the maximum level of the side lobes.
  Based on the data obtained, conclusions were drawn about the selection of the most suitable and
  demonstrating maximum performance windows, suitable for implementation on its basis of a controlled
  recursive low-pass filter with a finite impulse response.

• 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).

• 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.

• 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.

• IMPLEMENTATION OF AN EFFICIENT SEPARABLE VECTOR DIGITAL FILTER ON FPGA

  К.О. Sever, К.N. Alekseev, I.I. Turulin

  2024-08-12

  Abstract ▼

  In modern video surveillance systems, in which the use of computer vision technology is widespread,
  the most important information in the image is data on the contours of objects and the highlighting of small
  details. The systems are subject to stringent requirements, such as: high speed of processing information
  from a large number of cameras simultaneously, operation in conditions of poor lighting of the object and
  under the influence of external noise (electromagnetic fields, short interference from high-voltage transmission
  lines). Therefore, improving image processing methods using parallel computing devices and building a
  multi-threaded system is an urgent task. In this work, a 3x3 anisotropic high-pass filter is designed and simulated
  for image processing on an FPGA. An algorithm for its construction in the form of a separable vector
  representation is described. A detailed description is given of the development of an effective separable twodimensional
  digital filter for sharpening and highlighting the boundaries of objects in RGB images. The filter
  is based on the synthesis of the proposed 3x3 anisotropic high-pass filter and the Sobel gradient filter.
  The corresponding block diagram of the filter has been designed. Based on the results of processing the distorted
  image, we can conclude that the developed filter has the property of more uniform detailing and high lighting of objects in the image and is less susceptible to Gaussian noise compared to the Sobel gradient filter
  and the Laplace high-pass filter. A filter pipeline circuit has been developed on an FPGA for processing one
  plane of an RGB image. Due to the use of separable filters, the proposed implementation is almost 2 times
  more optimal in terms of the number of addition/subtraction operations performed than the direct implementation
  of a 3x3 Sobel gradient filter and a 3x3 anisotropic high-pass filter.

• TECHNIQUE FOR CONSTRUCTING THE STRUCTURE OF A RECURSIVE FILTER WITH A FINITE IMPULSE RESPONSE IN THE FORM OF A FUNCTION APPROXIMATING THE HANN WINDOW

  D.I. Bakshun, I.I. Turulin

  2024-08-12

  Abstract ▼

  Filters with an impulse response (IR) in the form of a weighting (smoothing) function are used in
  completely different areas of digital signal processing, such as spectral analysis - in order to reduce the
  Gibbs effect, in the formation of an amplitude distribution – to reduce the level of side lobes, including for
  radio engineering systems with synthesized aperture and others. The article considers the structure of a
  recursive FIR filter (RFIR-filter) with IR in the form of an approximated Hann window with a limited fixed
  number of multiplication and summation operations for any window duration. Such a structure has significantly
  lower computational complexity compared to the classical structure of the FIR-filter, and it can be
  used in embedded systems with limited computing resources. The function approximating the Hann window
  is a polynomial of the third degree, the coefficients of which are calculated using a specific integration
  of the quasi-sine function. An analytical formula is obtained for the coefficients of the non-recursive
  part of the filter by calculating the inverse finite difference of the fourth degree from the approximating
  function of the Hann window. The coefficients of the non-recursive part are integers, the values of which
  depend on the number of samples (length) of the half-cycle of the quasi-sine function, which simplifies the
  implementation of such an RFIR-filter based on a programmable logic integrated circuit (FPGA).
  The average absolute approximation error is calculated with an increase in the length of the window.
  When the number of samples is less than 600, the error does not exceed 4.5%, which is an indicator of the
  high accuracy of matching the approximating function to the Hann window. The authors propose a further
  perspective for the development of the structure of the RFIR-filter with IR in the form of an approximating
  function of the Hann window. This structure makes it possible to implement a RFIR-filter with a change in
  the length of the Hann window in the time domain while maintaining stability by accurately performing
  calculation operations using the coefficients of the non-recursive part, which are fixed-point numbers, and
  their linear dependence on the half-period length of the quasi-cosine function.

• RECURSPIVE SEPARABLE 2D DIGITAL FILTER FOR INCREASING THE SHARPNESS OF RGB IMAGES

  К. О. Sever, D.А. Guzhva, I.I. Turulin

  2024-01-05

  Abstract ▼

  An important role in the perception of image quality is sharpness, that is, the An important
  role in the perception of image quality is played by sharpness, that is, the magnitude of the brightness
  gradient in areas near the boundaries of objects. This characteristic is responsible for the
  clarity and detail of small image elements. Defocusing the camera lens and insufficient illumination
  are the main factors that can lead to digital image blurring. To increase the sharpness, various
  processing methods are used, such as filtering in the frequency domain, for example, the use of
  fast Fourier transform to emphasize the boundaries and textures of the image. The use of this typeof filtering allows you to control the contrast and frequency content of the image, which leads to
  an improvement in visual perception. However, this method has a number of significant drawbacks,
  such as logarithmic complexity and performing additional calculations associated with
  forward and inverse Fourier transforms. Therefore, the preferred method of image sharpening is
  the so-called spatial processing, which provides direct filtering of image pixels without additional
  transformations, and the reuse of processing results (recursive component) in the filter allows you
  to reduce the number of operations, reduce computational complexity. The article describes the
  development of an effective recursive separable two-dimensional digital filter to sharpen largedimensional
  RGB images. The algorithms of its construction are given, the corresponding block
  diagrams are designed. The filter has the property of more uniform detail of image objects, and is
  less susceptible to the creation of pulse noise. Also, for the original high-resolution RGB image, a
  blur filter is modeled, the matrix of which is filled according to the normal (Gaussian) law.
  To assess the filtration quality, the developed filter is compared with the algorithm of classical
  two-dimensional convolution with a 5x5 Laplace high-pass filter core.

• 8-BAND HETEROGENEOUS BANK OF FIR FILTERS WITH HIGH COMPUTATIONAL EFFICIENCY FOR HEARING AIDS

  D.А. Guzhva, К. О. Sever, I.I. Turulin

  2024-01-05

  Abstract ▼

  This article discusses recursive filters with finite impulse response and filter banks. The filter
  bank is an array of bandpass filters. The analysis filter block divides the input signal into several
  components, with each of the sub-filters carrying one frequency sub-band of the original signal.
  On the contrary, the synthesis filter block combines the output data of the sub-bands to restore
  the original input signal. In most applications, certain frequencies are more important than others.
  Filter blocks can isolate various frequency components in the signal. This way we can put more
  effort into processing more important components and less effort into processing less important
  components. Subband filters can be combined with step-down or step-up sampling to form a bank
  of multi-speed filters. Filter banks are widely used for speech recognition and speech quality improvement.
  Currently, filter banks have expanded their application to video and image processing.
  In addition, filter blocks are very useful in communication systems, including digital receivers and
  transmitters, pre-coding of filter blocks for channel alignment, discrete multi-tone modulation and
  blind channel alignment. The use of these filters for hearing aids is considered. An 8-band heterogeneous
  bank of recursive filters with finite impulse response (FIR) with high computational efficiency
  for hearing aids has been developed. The computational complexity (BC) of a recursive
  filter with a finite impulse response (RCIHF) is also compared with the computational complexity
  of non-recursive filters with a finite impulse response (NCIHF).

• COMPARATIVE EVALUATION OF AVERAGING METHODS FOR FILTERING MEASUREMENT SIGNALS

  V.G. Galaly, K.S.М. Al-Karawi, I.I. Turulin, S.А. Kirakosyan

  2023-06-07

  Abstract ▼

  To improve the quality of manufactured products, it is necessary to improve all technological
  processes, which requires increasing the accuracy of the entire measuring path as a whole.
  For this it is necessary to carefully analyze systematic, random and fluctuating errors in the measurement
  channel and take all measures to reduce them. Digital filtering or averaging of intermediate
  measurements (observations) according to certain rules is a radical means of improving the
  accuracy of measurements performed. The aim of this work is to compare the quality of suppression
  of near-real noise interference using the eight most well-known averaging methods. A model of the measurement path and a general block diagram for modeling the measurement process on a
  computer under the influence of random interference are proposed for eight averaging algorithms.
  As a criterion for evaluating the quality of averaging methods, the ratios of absolute error variances
  and mean square deviations before the computing device and after applying the specified averaging
  algorithm are taken. Based on the simulation results, the following conclusions are made. 1. All averaging
  algorithms provide suppression of random error components of complex interference to the
  level of 40–60 dB. Three algorithms are the best: arithmetic mean AR, a-truncated mean AU5 and atenderized
  mean AB5, which provide for the suppression of 5 % of anomalous results. With an increase
  in the number of observations, the suppression coefficients increase proportionally. 2. The
  sampling time must be a multiple of the duration of the 50 Hz AC mains period (20 ms). The optimal
  number of observations (measurements) is 100–128; with 128 measurements, the division operation
  is reduced to a simple shift, and the averaging result can be obtained in 1–2 μs. 3. When experimentally
  applying the AR averaging method for filtering a highly noisy measurement signal in a communication
  line with a length of 800 m, a decrease in the spread of ADC output codes was observed
  from ± 3.5 % to ± 0.1 % after filtering (AR, 64 measurements in 40 ms).