(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.

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.

Ultrasound physics is based on the fact that periodic motion emitted of a vibrating object causes pressure waves. Ultrasonic waves are made of high pressure and low pressure (rarefactional pressure) pulses traveling through a medium.

Properties of sound waves:

The speed of ultrasound depends on the mass and spacing of the tissue molecules and the attracting force between the particles of the medium. Ultrasonic waves travels faster in dense materials and slower in compressible materials. Ultrasound is reflected at interfaces between tissues of different acoustic impedance e.g., soft tissue - air, bone - air, or soft tissue - bone.
The sound waves are produced and received by the piezoelectric crystal of the transducer. The fast Fourier transformation converts the signal into a gray scale ultrasound picture.

The ultrasonic transmission and absorption is dependend on:
See also Sonographic Features, Doppler Effect and Thermal Effect.