Frequency Processing Ultrasound

In a blood vessel, blood components move with different velocities which are represented in the Doppler spectrum  . Three-dimensional Doppler frequency spectrum showing the distribution of individual Doppler shifts (amplitudes), flow directions (above and below the time axis), and flow velocities (computed from Doppler frequency shifts). The heights of the boxes correspond to the amplitudes of the respective Doppler frequencies. A Doppler frequency spectrum represents amplitudes by different levels of brightness. In color-coded duplex ultrasound (black boxes), the averaged flow velocity at a specific point in time is displayed in color according to the flow direction and superimposed on the two-dimensional grayscale image in real time. (According to P.M. Klews, in Wolf and Fobbe 1993) a range of frequencies with different amplitudes reflecting the distribution of flow velocities in the vessel. The technique that has established itself for spectral analysis is an algorithm known as fast Fourier transform (FFT), which breaks down the waveform into a series of sinusoidal waveforms. For the individual frequency values, the corresponding amplitudes are calculated and displayed in different shades of gray. According to Fourier’s theorem, any periodic waveform can be reconstructed from its component waveforms. Conversely, in spectral analysis, a complex waveform of a given frequency (Doppler shift frequency) is decomposed into its frequency components. In this case, the fast Fourier transform yields the amplitudes of the individual frequencies of the respective sine and cosine functions, which together make up the waveform. The individual frequencies thus separated are continuously displayed over time in the Doppler frequency spectrum (spectral waveform).

The Doppler spectrum contains the following information on blood flow  : vertical axis representing different flow velocities as Doppler frequency shifts, horizontal axis representing the time course of the frequency shifts, density of points, or color intensity, on vertical axis representing the number of red blood cells moving at a specific velocity (may also be plotted in the form of a histogram). Flow toward and away from the transducer is processed simultaneously and respectively represented above and below the baseline (zero flow velocity line). Alternatively, some ultrasound devices display the magnitudes of the different velocity components in a separate power spectrum. This is done by measuring the signal intensities of the individual Doppler frequencies at a specific time in the cardiac cycle and displaying the spectral distribution in a histogram. Doppler frequency spectrum of the superficial femoral artery (left section).The histogram plotted on the vertical axison the left represents the distribution of the different Doppler frequency shifts during systole. In the Doppler waveform, this distribution is represented by different levels of brightness (laminar flow). The right section shows the corresponding distribution during systole in the common carotid artery, which has less pulsatile flow