Doppler signals can be processed by using the Time-interval histogram method (TIH). This is not a formal spectral anaysis but will present as a somewhat "scale-down" effect as spectral anaysis. It can provide information about the shape of the waveform and its relationship to 'zero' blood flow. The disadvantage sof TIH however, are that the interfering noise is displayed with the flow signals. The strong lower frequency doppler signals may cause difficulty in distinguishing high frequency componenets. Arterial and venous components in the same signal may not be completely separated. Some of the disadvantages of TIH can be overcomed by 'Fast Fourier analysis'.

Jean Baptiste Fourier (1786- 1830) explained how a complex waveform could be built up using the superposition of an infinite sum of other less complex sinusoidal waveforms. Thus conversely, any nonsinusoidal or other complex waveform should be able to be decomposed into the less complex sinusoidal waveforms that combine to form the more complex waveform. Fourier analysis then is a mathematical tool for extracting knowledge of the underlying frequency spectrum in any signal.In a typical vascular doppler waveform processed by a Fourier spectrum analyser, which performs a Fast Fourier transform on the Doppler signal at intervals of approximately 10 ms, the amplitudes of the resulting spectra are encoded as brightnesses and these are plotted as a function of time (horizontal axis) and frequency shift (vertical axis) to provide a two-dimensional spectral display. With this technique, the range of blood velocities in the sample volume will produce a corresponding range of frequency shifts on the spectral display.

Fast Fourier analysis offers additional information, including direction of flow in vessel, and helped distinguish between laminar and turbulent flow. Subsequently, normal ranges of frequency values were established, and the FFT analysis of Doppler frequency became known as spectral analysis.

With Fast Fourier Transform, mean flow velocity, pulsatility index, and other diagnostic parameters can be displayed and measured. By comparing established typical values with actual examination results, the interpreter can make determinations about vessel hemodynamics. For example, stenoses and occlusions may cause elevated velocity levels. Mean velocity is representative of, but does not directly measure, blood flow in the vessel. Pulsatility index describes the shape of the waveform and the relationship between peak systole and end diastole. It is believed to represent, primarily, an estimation of downstream vascular resistance. Resistance Index provides another measure of downstream vascular resistance.

A paper on Fourier transformation can be found here.