Fast Hartley transforms for spectral analysis of ultrasound Dopplersignals

Spectral analysis of Doppler ultrasound is known to yield valuable information to assess the state of circulation in the peripheral blood vessels. In the past, the raw Doppler data have been directly input into a dedicated spectrum analyzer or transformed on a microcomputer using the fast Fourier transform (FFT) technique. In the present study, the first Hartley technique is used to transform on a microcomputer to the digitized Doppler data obtained from a normal common carotid artery is presented and the resulting spectra are compared to those obtained by using the Cooley-Tukey FFT algorithm. The Hartley transform has the advantages of being a purely real-numbered transform; therefore, for real Doppler data, it is not only more conceptually straightforward, but also requires less computer memory, is simpler to calculate, and is better suited to large-scale integration implementation. The raw Doppler data were input into a digital oscilloscope from the analog Doppler unit, digitized in real time with 12-b resolution, and displayed on the computer monitor. These data were then stored in a file, on floppy or hard disk, using software provided with the digitizing oscilloscope, and then transformed to the spectral domain using either transform technique. In this application, the transforms were performed using a compiled BASIC language