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The k-space domain and the space domain form a Fourier pair. Two pieces of information are found in each domain, the spatial information and the spatial frequency information. The spatial information, which is of great interest to all medical doctors, is seen as periodic functions in the k-space domain and is seen as the image in the space domain.
The inverse Fourier transform converts the frequency-domain function back to the time-domain function. A spectrum analyzer is a tool commonly used to visualize electronic signals in the frequency domain. A frequency-domain representation may describe either a static function or a particular time period of a dynamic function (signal or system).
A time-domain graph shows how a signal changes with time, whereas a frequency-domain graph shows how much of the signal lies within each given frequency band over a range of frequencies. Though most precisely referring to time in physics , the term time domain may occasionally informally refer to position in space when dealing with spatial ...
DSP engineers usually study digital signals in one of the following domains: time domain (one-dimensional signals), spatial domain (multidimensional signals), frequency domain, and wavelet domains. They choose the domain in which to process a signal by making an informed assumption (or by trying different possibilities) as to which domain best ...
where ν is the frequency of the wave, λ is the wavelength, ω = 2πν is the angular frequency of the wave, and v p is the phase velocity of the wave. The dependence of the wavenumber on the frequency (or more commonly the frequency on the wavenumber) is known as a dispersion relation.
The 50% cutoff frequency is determined to yield the corresponding spatial frequency. Thus, the approximate position of best focus of the unit under test is determined from this data. The MTF data versus spatial frequency is normalized by fitting a sixth order polynomial to it, making a smooth curve.
It is also occasionally referred to as temporal frequency for clarity and to distinguish it from spatial frequency. Ordinary frequency is related to angular frequency (symbol ω, with SI unit radian per second) by a factor of 2 π. The period (symbol T) is the interval of time between events, so the period is the reciprocal of the frequency: T ...
High-pass and low-pass filters are also used in digital image processing to perform image modifications, enhancements, noise reduction, etc., using designs done in either the spatial domain or the frequency domain. [6] The unsharp masking, or sharpening, operation used in image editing software is a high-boost filter, a generalization of high-pass.