Digital Signal Processing

Scientific & Technical

Digital Signal Processing No. 4-2018

In the issue:

- analysis of structures of IIR digital filters
- errors in magnitude response approximation
- nonlinear distortion in quantization
- object recognition on UAV flight trajectory
- methods for PAPR reduction
- cyclic autocorrelation function of the sequence Zadoff-Chu
- speech signal denoising
- stabilizing the level of false alarms
- algorithms to improve frequency resolution
- antenna selection in mimo systems
- phase errors in radar imaging systems

Minimum-of-maximum weighted error in magnitude response approximation of analog and digital classical filters
Mingazin A.T.
RADIS Ltd, Russia, Moscow, e

Keywords: magnitude response approximation, minimum-of-maximum weighted error, analog and digital classical filters.

On the website of Research Gate network W. Sinkala (Botswana Int. University of Science and Technology) asked a question: Is it possible to minimize the ripples in passband and stopband of an Elliptic function filter?.

The author of this paper answered that for this it is necessary to solve the algebraic equation of the fourth degree which includes elliptic functions and that this equation is bulky. Besides, a numerical example is given.

Since the answer attracted interest, and there is no definite answer on the raised question in literature, in the article more detailed generalized answer is given. It is shown that the solution is connected with finding of a minimum-of-maximum weighed error for the magnitude response approximation and really for this purpose it is necessary to solve the algebraic equation of the fourth degree which in turn under certain conditions addresses in the simple approximate formula. The received expressions are suitable not only for elliptic (Zolotarev Cauer) filters, but also for other classical analog and digital filters of Chebyshev and Butterworth with lowpass, highpass, bandpass and bandstop magnitude responses.


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4. Mingazin A.T. Extreme parameters of analog and digital filters // Elektrosvyaz, 1999, no. 1, pp. 22-23.

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Nonlinear distortion signals with amplitude modulation in quantization
Bryukhanov Yu.A., e-mail:
Lukashevich Yu.A.
, e-mail:
Yaroslavl Demidov State University, Russia, Yaroslavl

Keywords: amplitude modulation, quantization, spectral analysis, nonlinear distortion, coding, direct and complementary codes, demodulation, truncation, rounding.


The effects of quantization of signals with harmonic amplitude modulation on the nonlinear distortion of modulating signals for an arbitrary number of digits in the numbers representation and approximation for different methods of coding are investigated. Fractional arithmetic in direct or complementary codes with truncation or rounding were assumed for numbers' representation.The dependences of the modulated signal distortion factor on the number of digits, the method of coding and approximation of numbers, as well as on the value of the amplitude modulation coefficient are established.

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2. Bruhanov U.A., Lukashevich U.A. Nelineinye iskageniya garmonicheskih signalov pri kvantovanie // Padiotehnika, 2009, nomer 10, str. 57-60.

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4. Bruhanov U.A., Lukashevich U.A. Nelineinye iskageniya pri sigma-delita analogo-chifrovogo preobrazovaniya signalov // Padiotehnika and elektronika, 2017, tom 62, nomer 3, str. 224-233.

5. Bruhanov U.A. Metidika issledovaniya nelineinyh kolebaniy v sistemah diskretnogo vremeni pri pereodicheskih vozdeystviyah // Padiotehnika and elektronika, 2006, tom 51, nomer 2, str. 196-201.

6. Bruhanov U.A. Metod issledovaniya pereodicheskih prochessov v neavtonomnyh sistemah diskretnogo vremeni s kvantovaniem // Padiotehnika and elektronika, 2008, tom 53, nomer 7, str. 851-857.


Comparative analysis of four IIR filter structures
Mingazin A.T.
RADIS Ltd, Russia, Moscow, e

Keywords: IIR filter, roundoff noise-signal ratio, coefficient wordlength, cascade filter structures, filter structures based on all-pass networks, variation of initial parameters, a heuristic section allocation procedure.

The comparative analysis of the output roundoff noise-signal ratio and coefficient wor-dlength dependences from the filter order for fixed-point low-pass IIR filters is presented. wo cascade filter structures on the direct and optimal form sections and two filter structures based on all-pass networks on the direct and wave form sections are discussed. An one-parameter algorithm based on variation of initial parameters leads to the minimum coefficient wordlength. heuristic section allocation procedure built-in this algorithm minimizes the noise-signal ratio for the cascade filters.

Dependences of the output noise-signal ratio and coefficient wordlength from a filter order for a number of magnitude response requirements are presented. The analysis of these depen-dences allows to note the following:

It is possible to reduce significantly the coefficient wordlength and practically not to wor-sen or even to improve a little the noise-signal ratio by purposely increasing a filter order.

For cascade structures with edge frequencies close 0.5 and for structures based on all-pass networks with edge frequencies in all baseband there is not meaning to increase a filter order more than by two.

For edge frequencies close 0 or 0.5 the best results on two analyzed parameters are inherent to cascade structure on links of the optimal form.

For edge frequencies in the neighborhood of 0.25 the structures on links of the direct form and more - structure based on all-pass networks there is the advantage on the noise-signal ra-tio, and cascade structures - on longwise the coefficient wordlength. The advantage of cas-cade structures is lost with the requirement of very small passband ripple.

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6. Mingazin A.T. Noise, coefficient wordlenght and order of IIR filters // 20-th Int. Conf. Digi-tal signal processing and its applications, (DSPA-2018) vol.1, pp.208-213.

7. Mingazin A., Gordienko S., Gureev . IIR filter design: tolerance initial parameter space of Zoljtarev-Cauer filters // Components & Technologies, 2016, no. 10, pp.122-126.

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The object recognition on UAV flight trajectory by means of image parameters correction

Arzumanian E.P
Moscow Research Institute of Television, Russia, Moscow, e-mail:

Keywords: image, flight trajectory, template, video sequence, interpolation.

We consider a method that provides object recognition on the trajectory of UAV (unmanned aerial vehicle) in cases when the current image does not coincide with the reference image in scale, turning angle and aspect angle. To adapt said images with these parameters, a universal tool based on a bilinear interpolator is proposed. Proposed method provides the object identification on more long distances.

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Combined methods for PAPR reduction in the RAVIS system
Le Van Ky, postgraduate student, e-mail:

Dinh Thi Huyen Trang, postgraduate student, e-mail:
Multimedia technology and telecommunication department, MIPT, Russia, Moscow

PAPR, tone reservation, active constellation extension, selected mapping, combined method..

A well-known disadvantage of systems with OFDM modulation is a high Peak to Average Power Ratio (PAPR). Due to this feature OFDM radio signal contains a lot of short-term peaks, which requires the use of power amplifiers with a wide linear dynamic range. In this paper, we propose several combined methods of PAPR reduction in the digital terrestrial multimedia broadcasting system RAVIS.

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Investigation of the properties of cyclic autocorrelation function of the sequence Depending on the quantization characteristics of the elements of the sequence
T. P. Kiseleva, post-graduate student, e-mail:
Department of radio engineering systems of the Moscow technical University of communication and Informatics (MTUSI), Moscow, Russia

Keywords: OFDM , quantization, quantization step, number of quantization levels, quantizer characteristic, sequence of the Task (ZC), cyclic autocorrelation function (ACF).

The problem of quantization of sequences transmitted via broadband communication channels is determined by the need to reduce hardware and software costs and increase the speed of data processing in the construction of systems for receiving, transmitting and processing digital information. In modern systems, multi-digit signal structures with the number of 16, 32 or more digits are used. When operating with information that does not require high-precision computer calculations, there are no requirements for high-bit data, but often encouraged to improve the performance of the system along with the simplification of its hardware.

The article studies the properties of the cyclic autocorrelation function (ACF) of multilevel complex sequences of Zadoff - Chu used in current LTE OFDM technologies of modern communication systems, depending on the number of levels of quantization of elementary signal sequences in two versions: without considering quantization noises and taking into account these noises. Simulation of the sequence is performed In MATLAB at quantization levels of the real and imaginary parts of the sequence L=2,4,8,16,32,64.

The mathematical model of sequence Zadoff Chu cyclic autocorrelation of the sequence, the linear characteristics of the quantizer and the calculation formula for calculating the ratio of the square of the maximum of the ACF of the sequence Zadoff Chu to the average of the square of side lobes, the relationship module, the maximum value of the side lobe to the maximum of the ACF and graphs the ratio of the square of the maximum of the ACF quantized sequence Zadoff Chu to the average of the square of side lobes, depending on the characteristics of the quantization with and without allowance for the quantization noise.

The conclusions about the possibility of reducing the bit sequence Zadoff - Chu to 4 ... 6 digits. The ratio of the module of the maximum value of the side lobes to the maximum of the cyclic AKF increased from 1.33% at 64 quantization levels to 2.92% at 16 quantization levels, which opens up the possibility of using low-cost computing with low-bit data without significantly reducing the noise immunity of the generated sequences.

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Soft mask estimation technique using recurrent neural network for speech enhancement
Tupitsin G.S., e-mail:
Topnikov A.I., e-mail:
Yaroslavl Demidov State University, Russia, Yaroslavl

Keywords: speech signal, denoising, soft mask, recurrent neural network.

The problem of enhancing speech degraded by uncorrelated additive noise, when only the noised speech is available, has widely studied in the past and it is still in active field of research. Some methods in frequency domain using various spectral gain functions depending on a posteriori signal-to-noise ratio or/and a priori signal-to-noise ratio was proposed in the past.

The soft mask algorithm is similar to other algorithms in the frequency domain, but soft masks gain function is a probability of speech presence in each point of the time-frequency representation of the speech signal. An improved method for soft mask estimation using a recurrent neural network and an algorithm for suppressing noise in speech signals based on it was proposed in the paper. Compared with the previous version of the algorithm using the convolutional neural network, the network structure was changed, and the learning algorithm was revised. In the proposed version, the soft mask obtained via the Rayleigh distribution of amplitude noise spectrum in each frequency band is used as the target variable for neural network training algorithm.

A base of speech signals compiled from the records of the CHAINS speech corpus was used. For the training of the neural network 30 recordings were used (4 recordings per announcer), with a total duration of 1 hour 17 minutes 29 seconds. Testing was performed on the recordings of the remaining 6 speakers (34 recordings per speaker), with a total duration of 9 minutes and 12 seconds.

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Algorithm for stabilizing the level of false alarms with multi-frame accumulation of radar signals
Koshelev V.I., e-mail:
Belokurov V.A.
, e-mail:
The Ryazan State Radio Engineering University (RSREU), Russia, Ryazan

Keywords: multi-frame accumulation, CFAR, characteristic functions.

The paper considers the synthesis of the algorithm for stabilizing the level of false alarms with the multi-frame accumulation of reflected radar signals, which allows analytically calculating the detection threshold. A feature of the proposed algorithm is the use of the apparatus of characteristic functions, which makes it possible to calculate the detection threshold analytically excluding time-consuming numerical calculations of the convolution of distribution densities at each survey. At the final stage of the algorithm, linear interpolation of the dependence of the probability of a false alarm is performed. The effectiveness of the proposed algorithm is estimated by comparing the results of the analytical calculation of the detection thresholds and the thresholds obtained by the method of extremal statistics. Using simulation modeling, it is shown that the use of linear interpolation allows for a gain in the threshold signal-to-noise ratio of about 0.2 dB.


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Algorithm to improve spectral estimation
Tuyakov S.V., e-mail:
Joint-stock company Research and Production Enterprise SPETZ-RADIO, Russia, Belgorod

Keywords: algorithm, the discrete Fourier transform, the fast Fourier transform, computational complexity, approximation of the continuous Fourier transform, to improve spectral estimation.

The existing solution to the problem to improve spectral estimation is based on the use of the FFT algorithm to the data sequence supplemented with the necessary number of zeros (hereafter the classical algorithm) [1].

Algorithm to improve spectral estimation
Let's give a sequence of data designed for frequency analysis

where N equals a whole degree of two.

Through K we denote the coefficient of improvement of the spectrum evaluation, by which we will understand the increase in K times the sampling frequency of the continuous Fourier transformers.

The improvement factor K can be any natural number, large or equal to two

The DFT formula for fixed K looks like

The latter ratio is represented as a combination of K N-point DFT


For each L=0,...K-1, the DFT is implemented on the basis of the FFT algorithm with the corresponding coefficients.

The article concludes that the value of the analysis points shift on the frequency axis can be an arbitrary real number from the half-interval from [0;1), i.e. the following transformation is true

The last transformation allows for the sequence of fixed length data at different values r ∈ [0;1) to perform the sampling of continuous Fourier transformers with as small a sampling step as possible.

The algorithm proposed in the article to improve spectral estimation allows:
- Firstly, the continuous Fourier transformers can be sampled with as small a sampling step as you like,
- Secondly, to reduce the number of complex multiplications in relation to the classical algorithm,
- Thirdly, to implement calculations both in parallel and in sequential modes depending on the task being solved and the calculator's architecture.


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The advantages of antenna selection in MIMO systems versus conventional MIMO systems without antenna selection
V.B. Kreyndeylin, e-mail:
M.L. Khazov, e-mail:
Moscow Technical University of Communication and Informatics (MTUCI), Russia, Moscow

Keywords: spectral efficiency, noise resistance, antenna selection, communication channel capacity, radio channel, optimization criterion.

The article provides a comparative analysis of the noise immunity of general communication systems with many transmitting and many receiving antennas (Multiple-Input-Multiple-Output, MIMO) versus MIMO systems using Antenna Selection at the receiver and transmitter sides. In MIMO systems with Antenna Selection, the number of antennas for transmission and the number of antennas for signal receiving are greater than the number of transmit radiochains and the number of receive radiochains, respectively. The selection of antenna in each case is making out according to one of the algorithms using the given optimization criteria.

MIMO technology allow to significantly increase data transmission rates in wireless communications system without expanding of bandwidth of using communication system or increasing of transmitter power.

Using MIMO technology with a spatial multiplexing the high rate data symbol stream divides to many low rate sub-streams, which are transmitting in same time with different antennas.

General MIMO system has the number of transmit/receive chains equal to the number of transmission/receiving antennas respectively. Receiving and transmitting of carried signal carried out in same time at all transmitting and receiving antennas simultaneously on the same frequency.

In case of adding to MIMO system of one more antenna in pair with the additional path, we have increasing of noise immunity. However, this action increases the cost and complexity of the implementation of the communication system. The radio chains make general contribution to the cost and complexity of the communication system. Therefore, it is desirable to reduce their number.

So, it is very promising to use Antenna Selection algorithms, that allow to select a subset of transmit / receive antennas (depends on number of chains) among the available in communication system transmit / receive antennas.

Statistical simulation results given in this article show, that MIMO systems with Antenna Selection provide a significant power gain in comparison to conventional MIMO systems without Antenna Selection. Assessment of this power gain is given for various conditions and Antenna Selection criteria.


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The results of real-life experiments with Doppler sharpening algorithms and software: the analysis of phase errors in radar imaging systems
Valuyskiy D.V., 1
Vityazev S.V., 1, e-mail:
Androsov V.V., 2
Harin A.V., 1
Vityazev V.V. 1, e-mail:
Ryazan State Radio Engineering University (RSREU)1, Russia, Ryazan
Ryazan State Instrument-making Enterprise (RSIE)2, Russia, Ryazan

Keywords: radar imaging, phase errors, autofocus, PGA.

The problem pf autofocus in radar imaging systems is considered in this paper. The efficiency of one of the most popular autofocus techniques PGA is investigated for the implementation in a given system. The possibility of PGA autofocus is analyzed for the objects of different nature. The conclusion about PGA efficiency in case of such objects are made.


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