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This chemical shift error does not subtract in phase difference processing, but can be minimized with proper parameter selection.
By using the FEA-Newton algorithm, the relationship of the linewidth vs center frequency shift error and SNR vs center frequency shift error are both analyzed and the Brillouin center frequency shifts are extracted.
It propagates for example a Stokes wave of slope 0.2985 with a phase shift error of about 0.3° after 1000 periods of propagation.
For a bit error rate (BER) of 10−9, in order to make the additional received power penalty less than 0.5 dB, the phase shift error of each branch must be less than 2°.
It is second-order accurate with the same amplification factor and relative phase shift error as the original Lax Wendroff.
The rate between the sampling rate with the up sampling rate is sufficiently high and results in a low range shift error compared with the range bin.
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The chemical-shift displacement error between the two coupling partners of the lactate molecule leads to a signal decrease.
Compared to conventional Shinnar Le Roux pulses they lead to a decrease of the chemical-shift displacement error and consequently a lactate signal increase.
The chemical-shift displacement error is decreased and therefore the lactate signal is increased by using refocusing pulses with a broad bandwidth.
Computer simulations show that this method can depress both the amplitude error and the phase error simultaneously and significantly by 2 3 orders of magnitude for arbitrary irregular phase shift errors as large as up to 20% without the need of calibration or the knowledge of the actual phase shifts.
The amplitude and phase shift errors are within 15%% and 30°, respectively.
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