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“distance-Doppler” effect and applications. v. guruprasad inspired research. discovery applications locating isolating synthesis sample calculation realizability. premise empirical support status. contents. discovery. ω. r = 0. r. discovery. ω. r = 0. r. discovery. ω. ω 1.
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“distance-Doppler” effectand applications v. guruprasad inspired research
discovery applications locating isolating synthesis sample calculation realizability premise empirical support status contents
discovery ω r = 0 r
discovery ω r = 0 r
discovery ω ω1 r = 0 r1 r
ω ω1 ω2 r = 0 r1 r2 r discovery • frequency scaling effect • generic ~ Doppler • but asymmetric • α ~ at receiver • r ~ source distance • application classes • locating • isolating • synthesis (& analysis)
ω ω1 ω2 r = 0 r1 r2 r discovery • frequency scaling effect • generic ~ Doppler • but asymmetric • α ~ at receiver • r ~ source distance • application classes • locating • isolating • synthesis (& analysis) z3 z2 z1
ω ω1 ω2 r = 0 r1 r2 r discovery • frequency scaling effect • generic ~ Doppler • but asymmetric • α ~ at receiver • r ~ source distance • application classes • locating • isolating • synthesis (& analysis) z
ω ω2 r = 0 r2 r locating α3 α2 α1
ω ω1 r = 0 r1 r locating α3 α2 α1
ω ω1 ω2 r = 0 r1 r2 r locating • α:temporal parallax • in frequency domain • receiver-controlled • atan(α)∈ (- π/2, π/2) • ∆ω/ω ≡ z = α r • complementary: • spatial freq. • directional antennae α3 α2 α1
ω ω1 ω2 α3 α2 α1 -α1 r1 r2 location verification • special case α < 0 • narrows the spectrum • notch filter to verify r
locating applications • fast, precise, monostatic triangulation • half the round-trip delay • simpler, faster computation • infinite range of “parallax angles” • “true stealth radar” • where no phones go! • seeing = ranging • infinite range ~ P ∝ R-2 • “reverse-engineered” from astrophysics
received signal: F = F1 + F2 + F3 isolating “co-channel” sources at different distances your mission, should you accept it, is… F1 F2 F3 F
received signal: F = F1 + F2 + F3 isolating “co-channel” sources at different distances separate the signals without involving content or modulation! F1 F2 F3 F
received signal: F = F1 + F2 + F3 isolating “co-channel” sources at different distances H α 1. spread α α F1 F2 F3 F
received signal: F = F1 + F2 + F3 isolating “co-channel” sources at different distances H α G2 α α 2. filter F1 F2 F3 F
received signal: F = F1 + F2 + F3 isolating “co-channel” sources at different distances H α G2 α α H-1 3. down-scale F1 F2 F3 F
extracted signal: received signal: F = F1 + F2 + F3 H-1 G2 H F ≈ F2 isolating “co-channel” sources at different distances H α G2 α α H-1 F1 F2 F3 F receiver processing
isolating applications • distance-based selectivity • ~ directional antennae, polarizations • orthogonal to modulation • by physics of space • obviates TDM, FDM, CDMA • raises channel capacity to Rayleigh criterion • universal anti-jamming • even noise sources can be isolated out
α3 α2 α1 -α1 r1 r2 synthesis α1 optional signal ~ F1 μwave H(α) F3 F2 F0 F1 r r1
α3 α2 α1 -α1 r1 r2 synthesis α2 optional signal ~ F2 μwave H(α) F3 F2 F0 F1 r r1
F3 α3 F2 α2 α1 F1 -α1 r1 r2 synthesis α2 optional signal ~ F3 μwave H(α) F0 r r2
ω ω1 ω2 α3 α2 α1 -α1 r1 r2 synthesis optional signal tune α optical μwave H(α) F3 F2 F0 μwave source F1 r RF tune r
synthesis • precise control ~ r • infinite range ~ α • scales up or down • +α– up • - α – down • and generic • almost any waves • no nonlinear media • no b/w, freq. constraints optional signal tune α μwave H(α) r tune r
analysis • hi-fi down-scaling • even gamma rays • to μ-waves or RF • nifty analytical tool • if realizable tune α UV RF H(-α)
synthesis applications • universal wave sources • say using GW microwave sources • to yield THz, visible, UV or even gamma rays • modulation & coherence with power • without lasing • COTS-realizable • main constraint: source phase spectrum • expect better with non lasing photonic sources • e.g. z = 10 with r = 1 m easily using Terfenol-D
corrected: 2005-11-09 sample calculation • For z = 1 at r = 100 m, we need α = z / r = 1 / 100 m = 0.01 / m • From theory in paper, α≡ β / c , whereβ= normalized rate of change of grating or sampling intervals • We need β ≡ α c = 0.01 / m * 3x108 m / s = 3x106 / s, i.e. must vary the intervals by a factor of 3x106 every second! • But (a) variation is exponential, and (b) can be repeated over smaller intervals. • Same effective βpossible over intervals of 1 ns ≡ 1x10-9 s using e3E6 *1E-9≈ 1.0030045 • Max. change possible with Terfenol-D : 1.008 – 1.012
premise • wave speed independent of frequency • exceptions: dispersive media • realm of current research with phase & group velocities • sources of nonzero spectral spread • likely exceptions: CW carriers, lasers • spectral decomposition is receiver’s choice • exposes: usual Fourier assumptions • notably in quantum mechanics
receiver’s choice • spectral analysis or selection requires summing • summing is macroscopic • receiver can change during summing • general case is NOT Fourier decomposition • Fourier <=> absolutely zero change • zero change cannot be verified except by distant sources • error is Hubble’s law frequency shifts • overlooked in • all signal processing, spectrometry, even wavelets • all of astronomy & quantum physics
diffractive summing detector element static grating corresponding to time = t1 focal plane grating lens
diffractive summing detector element static grating corresponding to time = t2 focal plane grating lens
diffractive summing detector element static grating corresponding to time = t3 focal plane grating lens
summing by unsteady receiver younger rays (from t3) detector element instantaneous sum θ focal plane older rays (from t1) grating lens
summing by unsteady receiver younger rays (from t3) detector element n λ = l sin θ θ focal plane older rays (from t1) grating lens
n dλ = dl sin θ --- --- dt dt summing by unsteady receiver younger rays (from t3) detector element n λ = l sin θ θ focal plane older rays (from t1) grating lens
n dλ = dl sin θ --- --- dt dt summing by unsteady receiver younger rays (from t3) detector element n λ = l sin θ θ focal plane 1 dλ = 1 dl = -β -- --- -- --- older rays (from t1) λ dt l dt grating lens
time-varying receiver states t1 t2 changing receiver selection state... t3 time ...stationary in an expanding or shrinking reference frame
traditional receiver basis applied states incoming signal receiver states spectral window • receiver ~ spectral window of representative states • a state = a Fourier component mode that can be excited • a state = mode observed if excited • observation by a dot-product with states • as if the states were flowing into the receiver (left) • dot-product ≡ instant-by-instant product (right)
traditional receiver basis applied states incoming signal receiver states spectral window (inverted) • receiver ~ spectral window of representative states • a state = a Fourier component mode that can be excited • a state = mode observed if excited • observation by a dot-product with states • as if the states were flowing into the receiver (left) • dot-product ≡ instant-by-instant product (right)
evolving receiver basis applied states incoming signal receiver states spectral window time • when receiver window itself slides • relative to world frequency frame • incoming sinusoids appear expanding • own states appear steady
evolving receiver basis applied states time applied states incoming signal incoming waves receiver states spectral window spectral window ? time • when receiver window itself slides • relative to world frequency frame • incoming sinusoids appear expanding • own states appear steady • receiver states shorten in world frame • all states ~ same function (exponential λ) ~ in world frame • position in window identifies state
evolving receiver basis spectral window received component • Dot-product selects time-varying world wave • receiver states ~ exponential-λin world frame • dot-product ≡ instant-by-instant product • vanishes for sinusoid (broken line) • maximum for similar wave of same starting λ
evolving receiver basis spectral window received component • Dot-product selects time-varying world wave • receiver states ~ exponential-λin world frame • dot-product ≡ instant-by-instant product • vanishes for sinusoid (broken line) • maximum for similar wave of same starting λ
evolving receiver basis spectral window received component • Dot-product selects time-varying world wave • receiver states ~ exponential-λin world frame • dot-product ≡ instant-by-instant product • vanishes for sinusoid (broken line) • maximum for similar wave of same starting λ
evolving receiver basis applied states time applied states incoming signal selected waves receiver states spectral window spectral window time • when receiver window itself slides • selects exponential-λ wave components from world • selected wave components bear distance • λ∝ r or λ∝ r -1 • already well known in cosmology, thanks to…
Leonard Parker • Ph.D. thesis, Yale, ca. 1966 • particle wavefunctions in an expanding universe • leonard @ uwm . edu • But what do these eigenfunctions REALLY represent? • in their present incarnation as receiver states ?
spectral phase gradients • Green’s function theory • source = collection of radiating points • each radiating point ~ delta function • delta ~ same starting phases • consider their wave-vectors slopes ∝ distance
spectral phase gradients space part signal part ∆φ = ∆(k r – ω t) = r ∆k+ k ∆r – ∆(ω t)
spectral phase gradients space part signal part ∆φ = ∆(k r – ω t) = r ∆k+ k ∆r – ∆(ω t) k ∆r ~ holography, SAR, interferometry