|Digital Signal Processing||
Efficiency of product-codes turbo-decoding algorithms with different methods of information exchange between iterations
To describe standard algorithm consider product code concatenated serially from two block codes with lengths n1 and n2. Then code word of the product code may be considered as an n1 × n2 matrix, rows of which are code words of the first code and columns are code words of the second code. Turbo decoding is an iterative process consisting of carrying out a decoding of the rows followed by a decoding of the columns using soft-input soft-output (SISO) decoder of the corresponding component codes and reiterating this procedure several times. At each stage the decoder recalculates reliability estimation of each symbol, which form together n1 × n2 reliability matrix. Let Rkin and Rkout be input and output reliability matrixes at SISO stage number k. Then standard algorithm calculates the so called extrinsic information
The assessment of the significance of acoustic features in the task of detecting voice activity
Keywords: : speech signal, feature importance, voice activity detector, noise.
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As a nonlinear frequency modulation signal, signal with relatively low level of side lobes synthesized by author is used. Losses on weighting intime domain are absent for such signal.
In the offered detectors to stabilize of false detection probability, normalization of signal power to estimation mean signal power in running by length window, is used.
Due to great dependence of compressed nonlinear frequency modulation signal form on Doppler translation, it is offered to use a channel bank matched filter. Comparison of detectors efficiency is provided in wide range of Doppler frequencies.
It is obtained that using of detector of nonlinear frequency modulation signal and with a channel bank matched filter in all range of Doppler frequencies, is not efficient due to value of additional loss by detection of low-speed objects and also instrument cost, low efficiency when signals with different Doppler frequency collide.
It is offered to divide concerned Doppler frequency band (-140…140 KHz) on sub-bands and use different signal types and corresponding detectors in each sub-band.
To detect aerodynamic objects for Doppler frequencies -12,5…12,5 KHz in the absence powerful signals from local objects it is proposed to use the detector with nonlinear frequency modulation signal and single-channel matched filter. It is possible to obtain the gain of threshold signal value of 1,5…3,5 dB with respect to a non- weighted linear frequency modulation signal detector (with respect to a linear frequency modulation signal detector and weighting by Hamming – to 2 dB). A dual-channel linear frequency modulation signal detector is recommended in case of powerful signals from local objects.
In the case if Doppler frequencies of detected and/or overlapping in time band signals from objects lying in bands -140…12,5 KHz and 12,5…140 KHz, dual-channel linear frequency modulation signal detector is recommended. It is obtained that gain of nonlinear frequency modulation signal detector and with a single-channel matched filter might be 2…10 dB (power of filter input noise signal is 20 dB), and gain of nonlinear frequency modulation signal detector and with a multi-channel matched filter is 1…2 dB and more.
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The output discrete harmonic signal is calculated as the sum of the expansion coefficients of the harmonic function over the Walsh basis weighted by the values of the orthonormal basis of the discrete Walsh functions. The Walsh basis is easily generated from the current phase value produced by phase accumulator, with minor hardware cost by binary logical exclusive OR (XOR operation). Algorithm based on Gray code can be used to define the relationship between phase and any Walsh function. Formed Walsh functions are used as control signals for the signed inverters. The set of signed expansion coefficients is pre-calculated according to the direct discrete Walsh transform. The outputs of inverters are summed, forming the recovered cosine.
An example of cosine decomposition over Walsh basis, calculation and analysis of Walsh expansion coefficients are also given. Only a small part of the coefficients has considerable weight in the basis. The best criterion for selection of coefficients is the choice of the first N maximum coefficients by magnitude. The coefficient distribution by bit width demonstrates a way of the following simplification of phase-cosine converter.
The proposed Walsh and classical memory synthesizers were described by Verilog language and compiled for the FPGA xc7vx690tffg1761-2 of Virtex-7 family. The proposed Walsh phase-cosine converter requires about five times less resources compared to the classic memory phase-cosine converter at the same level of spurious free dynamic range more than 100 dB. The proposed Walsh direct digital synthesizer is recommended for implementation on programmable logic or application specific integrated circuits.
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The possibility of direct synthesis of digital IIR filters with complex selective requirements directly in an integer state space can be provided by the methodology integer nonlinear programming. This ideology allows for the efficient design of the integer recursive filters with a given number of bits represent data at the highest performance requirements of aggregate frequency characteristics of the filter at any form of their assignment.
This article discusses issues integral simulation and synthesis of recursive (IIR) digital filters taking into account the capacity to implement them on digital platforms with integer arithmetic calculations. The problem statement and solution of multifunctional synthesis of digital filters such a problem on the basis of the numerical methods of integer nonlinear mathematical programming are given. As an several typical examples, the problem solution of synthesis of IIR-filters with difficult selective requirements has been given. The analysis of their characteristics is resulted.
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In this paper a particular example is considered to illustrate the efficiency of various methods of digital bandpass filter (DBF) bank design. 64-channel filter system is designed with squareness ratio of filter amplitude-frequency characteristic α = 10 and the permissible deviations from the desired frequency response ε1perm=10-2 and ε2perm=10-3. The sampling frequency of the input complex signal ƒS = 10 kHz.
RT – the number of multiplication operations per time unit, S – the number of the data memory cells, τ – the delay time.
The analysis of the presented results of the costs calculation for the implementation of the DBF set with the frequency selection desired properties allows to draw the following conclusions.
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Adders of the digital system structure can create some quantization errors known as errors of overflow of adders. Cascade IIR filter structures with second order sections (SOS) are the most sensitive to these errors. Unlike FIR filter structures, overflow mode (Saturate or Wrap) for each sum in IIR filter structure will distort a result. The scaling allows preventing or minimizing errors of overflow.
Theoretical basis of scaling is known. However this basis does not consider many problems related to modeling the procedures by MATLAB. The report contains some additional interpretations of the existing theory allowing the user to realize the above mentioned modeling.
General principles of scaling procedures are described and main steps of scaling are substantiated. It is considered implementation of these principles for cascade structures with typical SOS: Direct-form I, Direct-form II, Direct-form I transposed, Direct-form II transposed. Each of scaling stages is illustrated by a specific SOS example with two sections. Calculation formulas for the Gains and Numerators after the scaling are derived.
The calculation of scaling factors is produced on the basis of the norm Linf for Magnitude Response. The general algorithm and his application are examined for cascade structures with typical SOS.
The paper illustrates the theoretical approach by results of IIR filter scaling using GUI FDATool.
General principles of normalizing Numerators and Gains are described and main steps of normalizing are substantiated. The paper illustrates the theoretical approach by results of IIR filter normalizing.
Simple MATLAB algorithm for calculation of the own noise variance of the cascade structure is proposed after the scaling. Calculation formulas for the own noise variance after the scaling are derived.
The cascade structure of IIR filters with known SOS structures and new Numerators is described as the dfilt object with the corresponding coefficient matrix. Coefficient matrixes of equivalent system functions are formed within the cycle by consecutive nullification of initial matrix elements. Equivalent impulse responses of cascade structure parts are calculated within the cycle with automatic limitations up to equal length. However coefficient matrices will differ before and after the scaling. As a result the own noise variance will be less after the scaling. The paper illustrates this effect for IIR filters with different SOS structures.
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