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Fixed-point data scaling in the matched filtering algorithm

Keywords:

O.V. Ershova – Programmer, «Scientific research centre of supercomputers and neurocomputers» Co Ltd. E-mail: ershova150681@mail.ru E.V. Kirichenko – Research Engineer, «Scientific research centre of supercomputers and neurocomputers» Co Ltd. E-mail: e.v.kirichenko@yandex.ru E.A. Semernikov – Head of Department, Department of Information Technologies and Control Processes, Southern Scientific Centre of RAS. E-mail: semernikov@mvs.tsure.ru A.V. Chkan – Research Engineer, «Scientific research centre of supercomputers and neurocomputers» Co Ltd. E-mail: chkan_andrey@mail.ru


The matched filtering operation in the digital signal processing systems is often carried out using the fast convolution algorithm that uses FFT and IFFT procedures. When using fixed-point arithmetic within the limitations of the digital array of hardware the data overflow on some iteration of the FFT and IFFT algorithms is possible. To solve this problem the scaling is performed consisting in the halving of the calculation results of the current iteration. In addition the total error of convolution calculation increases since the scaling error is added to the errors of rounding of the product of data multiplied by phase factors. Both excessive and insufficient scaling can lead to the decrease of the signal/noise ratio or even to a loss of useful signal in background noise. In the first case it occurs due to the growth of scaling errors, and in the second – as a result of overflow errors. Therefore from the standpoint of reducing of the total error of convolution calculation, scaling should be performed only in those cases where the overflow may occur. A method of adaptive normalization for determining the number of iterations with scaling of the FFT and IFFT algorithms depending on the energy of the input signal, convolution length, reference bandwidth and sampling frequency, as well as the number of bits of the system word length is proposed in this paper. The proposed method allows to estimate the number of scaling operations prior to convolution calculation and ensures the absence of overflows. A priori determination of the number of iterations with scaling is particularly important for the pipelining hardware implementation of the matched filtering device in which the results obtained in the previous iteration are immediately used in the next ones. This method can be used for creating the automatic scale setting means for the FFT and IFFT calculations with the fixed-point data in the matched filtering algorithm which is implemented by the fast convolution method.
References:

 

  1. Rabiner L., Gould B. Teorija i primenenie cifrovojj obrabotki signalov. M.: Mir. 1978. 847 s.
  2. LogiCORE IP Fast. Fourier Transform v9.0. Product Guide for Vivado. Design Suite. PG109. December 18, 2013. http://www.xilinx.com/ support/documentation/ip_documentation/ xfft/v9_0/pg109-xfft.pdf.

 

June 24, 2020
May 29, 2020

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