(FFT) The fast Fourier transformation is a particularly fast and efficient computational method of performing a Fourier transformation, which is the mathematical process by which raw data is processed into a usable image.
The fast Fourier transform analyzer is a common device that performs spectral analysis in ultrasound instruments. In this case, it displays different quadrature Doppler frequencies or reflector velocities when a sample volume cursor is used along time. The Doppler frequency is proportional to the spectral reflector velocity.

See also Proportionality Constant, and Sampling Rate.

A narrow or tuned Bandwidth describes a small frequency spectrum of pulses. With the Fourier transformation method a pulse or amplifier can be subscribed with its bandwidth. It is usually expressed with a 6dB drop of maximum amplitude, subscribing the bandwidth between the edges of the curve.
The selection of bandwidth is essential for achieving certain test results; narrow bandwidth for highly sensitive scans or broad banded for high resolution scans. The fast Fourier transformation uses beside the echo amplitude evaluation method the capability of the echo frequency / bandwidth information.

An integral is a mathematical object that can be interpreted as an area or a generalization of an area. A number computed by a limiting process in which the domain of a function, often an interval or planar region, is divided into arbitrarily small units, the value of the function at a point in each unit is multiplied by the linear or areal measurement of that unit, and all such products are summed (summation in the limit). In ultrasound imaging for example this mathematical function is used in the fast Fourier transformation.

Quadrature detection is used in Doppler ultrasound as well as in magnetic resonance imaging and is also called quadrature demodulation or phase quadrature technique. Quadrature detection is the acquisition of Mx and My simultaneously as a function of time by using two separate detector channels. This signal processing method is used for directional Doppler in which the signal reference frequency for the two channels has a phase shift of 1/4 period. The output Doppler signal phase for both channels also depends on the Doppler shift whether positive or negative.
The fast Fourier transform analyzer performs spectral Doppler analysis in ultrasound machines and displays different quadrature Doppler frequencies, when a sample volume cursor is used along time.

Spectral Doppler refers to the combination of either continuous wave Doppler or pulsed Doppler with a spectral display. Spectral Doppler provides a quantitative analysis of the velocity and direction of blood flow.
The Fourier spectrum analyzer performs a fast Fourier transformation on the Doppler signal. The amplitudes of the resulting spectra are encoded as brightness. In the 2D spectral display, the frequency shift is depicted in the vertical and the time in the horizontal axis. The range of blood velocities in the volume produces a corresponding range of frequency shifts.

See also Acceleration Index and Triplex Exam.