|Digital Signal Processing||
Minimum-of-maximum weighted error in magnitude response approximation of analog and digital classical filters
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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Nonlinear distortion signals with amplitude modulation in quantization
Keywords: amplitude modulation, quantization, spectral analysis, nonlinear distortion, coding, direct and complementary codes, demodulation, truncation, rounding.
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Comparative analysis of four IIR filter structures
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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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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The soft mask algorithm is similar to other algorithms in the frequency domain, but soft mask’s 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.
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Algorithm to improve spectral estimation
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.
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The advantages of antenna selection in MIMO systems versus conventional MIMO systems without antenna selection
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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