Page 1 Noise Reducion/Mode Isolaion wih Adapive Down Conversion (ADC) Abel B. Diaz, Thomas W. Tunnell NSTec Los Alamos Operaions Presened o PDV Workshop 8-16-2007
Page 2 Summary Adapive down conversion (ADC) analysis mimics down conversion in radio frequency (RF) quadraure daa acquisiion. ADC differs from he RF quadraure applicaion by using a ime-dependen mixing frequency. Curren ADC applicaion uses he frequency (i.e., velociy) exraced from he Fas Fourier Transform (FFT) specrogram analysis. For he daa analysis, he low-pass filering sep decreases band widh noise and isolaes he seleced mode (i.e., he mode from which he velociy was exraced in he FFT specrogram). Following he RF quadraure procedure, addiional analysis seps reconsruc he isolaed mode and is quadraure daa se ha is roaed 90. Phases, frequencies, and velociies are hen compued in sandard procedure. This echnique is applicable o quadraure and riaure phoon Doppler velocimey (PDV). Applicaion o Thermos Confirmaory daa from PRAD is presened.
Page 3 Radio Frequency Down Conversion I Reconsrucion () = i( ) cos( 2πf 0) + q( ) sin( 2πf 0) () = i() sin( 2πf 0) q() cos( 2πf 0) 1 Q() () Φ = an I Q
Page 4 Adapive Down Conversion Replace 2πf wih φ = π dτ m 2 f FFT And eliminae A/D V () = π λ 4 dφ() d
Page 5 Thermos Confirmaory Daa from PRAD The velociy calculaion based on he unfolding of he phase funcion is more sensiive o noise han he power basis of he FFT specrogram. The decrease in signal around 2, 2.5, and 3 μs indicaes large uncerainies in velociy calculaions.
Page 6 FFT Velociies for PDV Confirmaory Daa from PRAD The legend refers o FFT window; FFTs compued wih Hanning window. The shorer windows provide beer ime resoluion, while he larger windows provide beer frequency resoluion. Velociy, m/s The phase-based calculaions have promise o improve ime resoluion, bu are more sensiive o noise han he power-based FFT approaches. ADC was developed for mode isolaion and o improve signal-onoise raio in he phase-based calculaions. Sample resuls of improving signal-o-noise and mode isolaion (i.e., eliminaing unwaned modes) is shown nex.
Page 7 Noise and Low-Frequency Modes Zoomed view a shock break ou These daa were high-pass filered a 30 MHz and low-pass filered a 600 MHz. Sufficien noise remains o disor peaks, roughs, and he wave form in general. Zoomed view a 2 microseconds Sufficien low-frequency modes persis o elevae some minima above some maxima. Would be a problem for riaure daa ses as well.
Page 8 Zoomed View of Same Regions These plos show subsanial noise reducion and mode isolaion ha were achieved wih ADC. Sample plos of ADC velociies are shown nex.
Page 9 Velociies Compued Using ADC, 1 Velociy, m/s Legend idenifies he FFT calculaion from which he frequency, f () = v /(λ/2), is used o generae he mixing funcion. Daa are processed wih a 22 MHz band pass (+/- 15 m/s) and 1-ns smoohing in he calculaion of he ime derivaive. Wih noable excepions (he 2, 2.5, and 3 μs), he ADC resuls are in beer agreemen han he FFT calculaions. The nex viewgraph zooms in on he shoulder.
Page 10 Velociies Compued Using ADC, 2 Zoomed view of shoulder. In general, analysis resuls wihin 1 2 m/s agreemen. Velociy, m/s The nex viewgraph zooms in on he shoulder wih 10-ns smoohing.
Page 11 Velociies Compued Using ADC, 3 Zoomed view of shoulder. In general, analysis resuls wihin 1 m/s agreemen wih greaer smoohing. Velociy, m/s Model for uncorrelaed errors (nex) predics greaer agreemen. We suspec ha addiional smoohing is limied by naural bandwidh in he daa.
Page 12 Error Model (Uncorrelaed) ( ) Δ + Δ = 2 2 2 2 3 2 1 1 12 N S N N v v E ω δ δ velociy error - velociy - - angular frequency fringe - fracional 2 o noise - signal - sample inerval jier ime - v v v N S δ ω π ω δ Δ Δ Recording sysem Daa Analysis
Page 13 Thermos Confirmaory Daa Error Conours for 5 % Accuracy
Page 14 Conclusion ADC calculaions depend on prior esimae of velociy of signal. The velociies from he FFT specrogram appear o be a good esimae from which o calculae mixing phase. ADC provides effecive noise reducion and mode isolaion. For he Thermos Confirmaory daa, analysis is probably limied by naural bandwidh of he signal (1 2 m/s). ADC has been inegraed ino a user inerface ha includes sandard FFT analysis. ADC has already been applied o riaure daa for mode isolaion and noise reducion. Some invesigaions of he low-pass filered daa ses, i() and q(), may be warraned.