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The image sampling frequency is the repetition rate of the sensor integration period. Since the integration period may be significantly shorter than the time between repetitions, the sampling frequency can be different from the inverse of the sample time: 50 Hz – PAL video; 60 / 1.001 Hz ~= 59.94 Hz – NTSC video
where is the sampling time (the reciprocal of sampling frequency), is the duration of G PE, ¯ (gamma bar) is the gyromagnetic ratio, m is the sample number in the FE direction and n is the sample number in the PE direction (also known as partition number).
For a given sampling rate (samples per second), the Nyquist frequency (cycles per second) is the frequency whose cycle-length (or period) is twice the interval between samples, thus 0.5 cycle/sample. For example, audio CDs have a sampling rate of 44100 samples/second. At 0.5 cycle/sample, the corresponding Nyquist frequency is 22050 cycles/second .
Efficient k-space sampling also decreases data collection time. Rectilinear scanning has become the standard k-space sampling method for MRI. [14] However, the process takes a relatively long time as it samples the entire k-space equally. Because of this delay, other sampling methods are used to capture real-time motion.
For radial data sampling, the phase- and frequency-encoding gradients are replaced by two simultaneously applied frequency-encoding gradients that rotate the Fourier lines in data space. [ 1 ] [ 3 ] In either case, repetition times are as short as 2 to 10 milliseconds, so that the use of 64 to 256 repetitions results in image acquisition times ...
The reason for mainly affecting data sampling in the phase-encoding direction is the significant difference in the time of acquisition in the frequency- and phase-encoding directions. [1] Frequency-encoding sampling in all the rows of the matrix (128, 256 or 512) takes place during a single echo (milliseconds).
Music, for instance, may contain high-frequency components that are inaudible to humans. If a piece of music is sampled at 32,000 samples per second (Hz), any frequency components at or above 16,000 Hz (the Nyquist frequency for this sampling rate) will cause aliasing when the music is reproduced by a digital-to-analog converter (DAC). The high ...
The sampling theorem states that sampling frequency would have to be greater than 200 Hz. Sampling at four times that rate requires a sampling frequency of 800 Hz. This gives the anti-aliasing filter a transition band of 300 Hz ((f s /2) − B = (800 Hz/2) − 100 Hz = 300 Hz) instead of 0 Hz if the sampling frequency was 200 Hz. Achieving an ...