Exact(2)
Note that in order to ensure purely imaginary outputs, x[0] and (x[frac {N}{2}]) should be equal to 0. Therefore, these two signals can also be removed.
The and in (4) are the sampled real and imaginary outputs of the convolution between and the baseband channel impulse response, respectively, and are the noise in I- and Q- branches, respectively.
Similar(58)
After the 2D FT, spectra were converted to power estimates by adding the real squared to the imaginary squared output from the 2D FT. No phasing was necessary for the final FT output due to phasings/frequency shift corrections after the 1st FT to correct for phase imperfections/instabilities of the scanner.
After pushing the twiddle factors, the top output of the butterfly can be obtained by appending the 2 inputs, since the top input is purely real and the bottom input is purely imaginary; the bottom output can be eliminated, as it is conjugate symmetric to the top output.
The synthesis filter bank is just like the analysis filter bank complex-valued, however the imaginary part of the output signal is discarded.
SCS-MMA achieves equalization by forcing the real and imaginary parts of equalizer output onto a four-point contour with distance R 2 from the origin.
As a result the imaginary component of the output vector after the Fourier transform in algorithm 2 will be zero (or a very close value to it owing to the approximate floating number arithmetic) and, unlike the first algorithm, the dropping of the imaginary part will therefore not represent a loss of information.
this P Q noise is reduced to [20] P_{Q}leq frac{{d_{s}^{2}}}{6}(log_{2}N-2) (11). in the real and imaginary parts of all FFT outputs.
Although the quantization noise power in all real and imaginary parts of the DFT outputs is estimated in [20] as P_{Q}=Nfrac{{d_{s}^{2}}}{12} (10).
An optimized simultaneous compression and encryption method is applied simultaneously on the real and imaginary components of the DRPE output plane.
However, including both real and imaginary parts of the equalizer output in the cost function and equalizing them separately sometimes results in diagonal solutions [29].
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