# The MR signal is a time varying magnetic field, which has amplitude, frequency and phase and induces a time varying electrical field in the receiver coil, which also has amplitude, frequency and phase. This analog signal is sampled digitally over time using an A2D. Thus, while the overall signal does have amplitude, frequency and phase, each digital sample is simply a measure of amplitude collected at a point in time. Actually, the signal is recorded is the envelope of amplitude present over a period of time during which we record one sample (I.e., Ts). This measure of signal amplitude is written to a point in memory and the points in memory are in time sequence. This is called the time domain data. As I repeatedly emphasize in the videos, each sample derives from the entire MR signal, which arises from the entire slice we have excited. Thus, none of these samples correspond to any specific spatial location in the slice. Spatial information must be extracted by the Fourier transform.

# When the signal is sampled using two coils (e.g., a quadrature coil to improve SNR), we actually have two signals, which are phase shifted. These are traditionally referred to as the “real” and “imaginary” components and their vector sum is the magnitude of the net MR signal. This magnitude signal is what is written into each point in k-space and, consequently, there is one point in k-space for each sample recorded in the time domain data. Thus, the k-space samples could be plotted to approximate the frequency and phase of the original analog signal. Note that any given data point in k-space does not itself contain frequency or phase information, only amplitude. I addition to the combination of component (e.g. Real and imaginary) signals, other processing such as filtering may be applied to the MR signal before k-space has the form on which we apply the Fourier transform.

# Lastly, the phase of the MR signal can be computed from the two components (real and imaginary) to quantify the phase of the signal. If this information is entered into k-space (i.e., the value recorded in k-space is the computed phase), an image can be created that reflects phase of the MR signal at each voxel.

# For an excellent summary, see Allen Elster’s discussion here.