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Channel Estimation Techniques in the MIMO-OFDM System
Published in Mohammed Usman, Mohd Wajid, Mohd Dilshad Ansari, Enabling Technologies for Next Generation Wireless Communications, 2020
Asif Alam Joy, Mohammed Nasim Faruq, Mohammad Abdul Matin
Let the corresponding received transmitted samples be y(0), y(1), y(3), y(4)………y(n). Now a serial-to-parallel operation is carried out, i.e., DEMUX at the output of the Demultiplexer. Then the FFT operation at the receiver is performed. The outputs of the FFT block are Y(0), Y(1), Y(2), Y(3)……. Y(N). After taking the FFT operation of the circular convolution, it becomes the multiplication in the frequency domain. FFTy=FFTh.FFTx+FFTv⇒Yk=HkXk+Vk
Digital Signal Processing
Published in Richard C. Dorf, Circuits, Signals, and Speech and Image Processing, 2018
W. Kenneth Jenkins, Alexander D. Poularikas, Bruce W. Bomar, L. Montgomery Smith, James A. Cadzow, Dean J. Krusienski
Most of the properties listed in Table 14.5 for the DFT are similar to those of the Z-transform and the DTFT, although there are some important differences. For example, Property 5 (time-shifting property) holds for circular shifts of the finite length sequence s[n], which is consistent with the notion that the DFT treats s[n] as one period of a periodic sequence. Also, the multiplication of two DFTs results in the circular convolution of the corresponding DT sequences, as specified by Property 7. This latter property is quite different from the linear convolution property of the DTFT. Circular convolution is simply a linear convolution of the periodic extensions of the finite sequences being convolved, where each of the finite sequences of length N defines the structure of one period of the periodic extensions.
MATLAB Applications to Engineering
Published in José Miguel, David Báez-López, David Alfredo Báez Villegas, ® Handbook with Applications to Mathematics, Science, Engineering, and Finance, 2019
José Miguel, David Báez-López, David Alfredo Báez Villegas
The circular convolution of two sequences is obtained by multiplying the DFT of the sequences. Thus for the sequences x1(n) and x2(n) of Example 10.6 we have >> x1 = [1 2 3 4 5 4 3 2 1]; >> x2 = [1 2 -1]; >> F1 = fft(x1) F1 = Columns 1 through 3 25.0000 -7.7909 -2.8356i 0.2169 + 0.1820i Columns 4 through 6 -0.5000 -0.8660i 0.0740 + 0.4195i 0.0740 - 0.4195i Columns 7 through 9 -0.5000 +0.8660i 0.2169 - 0.1820i -7.7909 + 2.8356i >> F2 = fft(x2) F2 = 2.0000 0.5000 - 2.5981i 0.5000 + 2.5981i
Novel fluctuation reduction procedure for nuclear reactivity calculations based on the discrete fourier transform method
Published in Journal of Nuclear Science and Technology, 2019
Daniel Suescún-Díaz, Jaime H. Lozano-Parada, Diego Alejandro Rasero-Causil
A new method to reduce fluctuations in the calculation of nuclear reactivity using the inverse point kinetic equation was presented. Our method is based on a discrete version of the Fourier transform that can perform a circular convolution through the implementation of the fast Fourier transform (FFT). This method resolves the neutron population density history with a zero – order approximation, which is improved with the trapezoidal approximation to meet the criticality condition. In order to reduce fluctuations, a first-order delay low-pass filter and a Savitzky-Golay filter were used, assuming that the measured neutron population density has a Gaussian noise distribution around the average neutron population density with a standard deviation of up to σ = 0.01 and with calculation times up to t = 0.1 s. The best results are obtained using the FFT and a Savitzky-Golay filter with different numbers of filterings of the neutron population density history.