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Frequency Encoding
Encoding the distribution of sources of MR signals along a direction in space with different frequencies. In general, it is necessary to acquire a set of signals with a suitable set of different frequencies in order to reconstruct the distribution of the sources along the encoded direction. In the absence of other position encoding, the Fourier transformation of the resulting signal is a one-dimensional projection profile of the object.
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Frequency Encoding Gradient
(Gf) A frequency encoding gradient produces a magnetic gradient field present during MR signal acquisition to encode signals into different frequencies, depending on their position toward the gradient.
Also called readout gradient.

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BandwidthForum -
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(BW) Bandwidth is a measure of frequency range, the range between the highest and lowest frequency allowed in the signal. For analog signals, which can be mathematically viewed as a function of time, bandwidth is the width, measured in Hertz of a frequency range in which the signal's Fourier transform is nonzero.
The receiver (or acquisition) bandwidth (rBW) is the range of frequencies accepted by the receiver to sample the MR signal. The receiver bandwidth is changeable (see also acronyms for 'bandwidth' from different manufacturers) and has a direct relationship to the signal to noise ratio (SNR) (SNR = 1/squareroot (rBW). The bandwidth depends on the readout (or frequency encoding) gradient strength and the data sampling rate (or dwell time).
Bandwidth is defined by BW = Sampling Rate/Number of Samples.
A smaller bandwidth improves SNR, but can cause spatial distortions, also increases the chemical shift. A larger bandwidth reduces SNR (more noise from the outskirts of the spectrum), but allows faster imaging.
The transmit bandwidth refers to the RF excitation pulse required for slice selection in a pulse sequence. The slice thickness is proportional to the bandwidth of the RF pulse (and inversely proportional to the applied gradient strength). Lowering the pulse bandwidth can reduce the slice thickness.

Image Guidance
A higher bandwidth is used for the reduction of chemical shift artifacts (lower bandwidth - more chemical shift - longer dwell time - but better signal to noise ratio). Narrow receive bandwidths accentuate this water fat shift by assigning a smaller number of frequencies across the MRI image. This effect is much more significant on higher field strengths. At 1.5 T, fat and water precess 220 Hz apart, which results in a higher shift than in Low Field MRI.
Lower bandwidth (measured in Hz) = higher water fat shift (measured in pixel shift).
See also Aliasing, Aliasing Artifact, Frequency Encoding, and Chemical Shift Artifact.


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Gradient Recalled Echo SequenceInfoSheet: - Sequences - 
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The gradient recalled echo MRI sequence generates gradient echoes as a consequence of echo refocusing. The initial slice selective RF pulse applied to the tissue is less than 90° (typically rotation angles are between 10° and 90°). Immediately after this RF pulse, the spins begin to dephase.
Instead of a refocusing 180° RF pulse, reversing the gradient polarity produces a gradient echo. A negative phase encoding gradient and a dephasing frequency encoding gradient are used simultaneous. The switch on of the frequency encoding gradient produces an echo caused by refocusing of the dephasing, which is caused by the dephasing gradient.
TR and flip angle together control the T1, and TE control T2* weighting.

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Readout Gradient
Magnetic field gradient applied during the period when the receiver components are on. The application of this gradient, which is active during the period when the echo is being formed, results in the frequency encoding of the object being imaged.
Also called frequency encoding gradient.

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