Analytical and Experimental Comparisons Between the Frequency-Modulated-Frequency-Shift Measurement and the Pulsed-Wave-Time-Shift Measurement Doppler Systems

In previous publications, a new echo-ranging Doppler system based on transmission of repetitive coherent frequency-modulated ͑FM͒ sinusoids in two different implementations was presented. One of these implementations, the frequency-modulated–frequency-shift measurement ͑FM–fsm͒ Doppler system is, in this paper, compared with its pulsed-wave counterpart, the pulsed-wave– time-shift measurement ͑PW–tsm͒ Doppler system. When using transmitted PW and FM signals with a Gaussian envelope, the parallelism between the two systems can be stated explicitly and comparison can be made between the main performance indices for the two Doppler systems. The performance of the FM and PW Doppler systems is evaluated by means of numerical simulation and measurements of actual flow profiles. The results indicate that the two Doppler systems have very similar levels of performance. LIST OF SYMBOLS B 0 ϭf 2 Ϫ f 1 , frequency excursion of transmitted signal B rms rms bandwidth of transmitted signal D nominal range ⌬D axial range cell distance defined by signal processing d (n) ϭd (0) ϩ␯nT r , range of scatterer at the onset of nth transmission f 0 center frequency of transmitted signal; for FM: f 0 ϭ(f 1 ϩ f 2)/2 f 1 ''start'' instantaneous frequency of transmitted sweep signal ͑@tϭ0͒ f 2 ''stop'' instantaneous frequency of transmitted sweep signal ͑@tϭt m ͒ ⌬ f a ϭ␶ 0 S 0 , change in position frequency between two consecutive fsm spectra f a (n) ϭ͑t (n) Ϫt s)S 0 , position ͑or center͒ frequency of the fsm spectrum f w ϭ(2⌬D/c)S 0 , width of spectral window in fsm signal processing S 0 ϭB 0 /t m , sweep rate of transmitted FM signal t (n) ϭ2d (n) /c, ultrasound round trip travel time for scat-terer at the onset of transmission number n t a (n) measure of rate of oscillations of the nth spectral cross-correlation function in the FM–fsm Doppler system t d (n) ϭt (n) Ϫt, difference between acoustic delay (t (n)) and system delay (t s) t m time duration of transmitted signal T r pulse or sweep repetition time t s ϭ2D/c, time delay corresponding to nominal range T w ϭ2⌬D/c, duration of time window in tsm signal processing ␯ velocity component of target ͑scatterer͒ along ultra-sound beam ␯ alias aliasing velocity in a psm Doppler system ␣ form factor for Gaussian envelope ␣ G ϭ2͑␣/t m ͒ 2 , combined form factor ␤ ϭ(cϪ␯)/(cϩ␯), Doppler compression factor ␥ frequency …