milcom 2005 (sigint us-only) “distance-doppler” effect and applications v. guruprasad inspired...
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MILCOM 2005 (SIGINT US-only)
““distance-Doppler” effectdistance-Doppler” effectand applicationsand applications
v. guruprasadv. guruprasad
inspired researchinspired research
2005-10-182005-10-18 22(c) 2005 V. Guruprasad. All rights reserved.(c) 2005 V. Guruprasad. All rights reserved.
MILCOM 2005 (SIGINT US-only)
contentscontents
discoverydiscovery
applicationsapplications locatinglocating isolatingisolating synthesissynthesis
sample calculationsample calculation realizabilityrealizability
premisepremise
empirical supportempirical support
status status
2005-10-182005-10-18 33(c) 2005 V. Guruprasad. All rights reserved.(c) 2005 V. Guruprasad. All rights reserved.
MILCOM 2005 (SIGINT US-only)
discoverydiscovery
r = 0 r
ω
2005-10-182005-10-18 44(c) 2005 V. Guruprasad. All rights reserved.(c) 2005 V. Guruprasad. All rights reserved.
MILCOM 2005 (SIGINT US-only)
discoverydiscovery
r = 0 r
ω
2005-10-182005-10-18 55(c) 2005 V. Guruprasad. All rights reserved.(c) 2005 V. Guruprasad. All rights reserved.
MILCOM 2005 (SIGINT US-only)
discoverydiscovery
r = 0 r1 r
ω ω1
2005-10-182005-10-18 66(c) 2005 V. Guruprasad. All rights reserved.(c) 2005 V. Guruprasad. All rights reserved.
MILCOM 2005 (SIGINT US-only)
discoverydiscovery
frequency scaling effectfrequency scaling effect generic generic ~ Doppler~ Doppler but but asymmetricasymmetric
• αα ~ ~ at receiverat receiver• rr ~ source distance ~ source distance
application classesapplication classes locatinglocating isolatingisolating synthesis (& analysis)synthesis (& analysis)
r = 0 r1 r2 r
ω ω1 ω2
2005-10-182005-10-18 77(c) 2005 V. Guruprasad. All rights reserved.(c) 2005 V. Guruprasad. All rights reserved.
MILCOM 2005 (SIGINT US-only)
discoverydiscovery
frequency scaling effectfrequency scaling effect generic generic ~ Doppler~ Doppler but but asymmetricasymmetric
• αα ~ ~ at receiverat receiver • rr ~ source distance ~ source distance
application classesapplication classes locatinglocating isolatingisolating synthesis (& analysis)synthesis (& analysis)
r = 0 r1 r2 r
ω ω1 ω2
z3
z2
z1
2005-10-182005-10-18 88(c) 2005 V. Guruprasad. All rights reserved.(c) 2005 V. Guruprasad. All rights reserved.
MILCOM 2005 (SIGINT US-only)
discoverydiscovery
frequency scaling effectfrequency scaling effect generic generic ~ Doppler~ Doppler but but asymmetricasymmetric
• αα ~ ~ at receiverat receiver• rr ~ source distance ~ source distance
application classesapplication classes locatinglocating isolatingisolating synthesis (& analysis)synthesis (& analysis)
r = 0 r1 r2 r
ω ω1 ω2
z
2005-10-182005-10-18 99(c) 2005 V. Guruprasad. All rights reserved.(c) 2005 V. Guruprasad. All rights reserved.
MILCOM 2005 (SIGINT US-only)
locating locating
r = 0 r2 r
ω ω2
α1
α2α3
2005-10-182005-10-18 1010(c) 2005 V. Guruprasad. All rights reserved.(c) 2005 V. Guruprasad. All rights reserved.
MILCOM 2005 (SIGINT US-only)
locating locating
r = 0 r1 r
ω ω1
α1
α2α3
2005-10-182005-10-18 1111(c) 2005 V. Guruprasad. All rights reserved.(c) 2005 V. Guruprasad. All rights reserved.
MILCOM 2005 (SIGINT US-only)
locating locating
αα:: temporal parallaxtemporal parallax in frequency domainin frequency domain receiver-controlledreceiver-controlled atan(α) ∈ (- π/2, π/2) ∆ω/ω ≡ z = α r
complementary:complementary: spatial freq.spatial freq. directional antennaedirectional antennae
r = 0 r1 r2 r
ω ω1 ω2
α1
α2α3
2005-10-182005-10-18 1212(c) 2005 V. Guruprasad. All rights reserved.(c) 2005 V. Guruprasad. All rights reserved.
MILCOM 2005 (SIGINT US-only)
location verificationlocation verification
special case special case αα < 0 < 0 narrows the spectrumnarrows the spectrum notch filter to verify notch filter to verify rr
r1 r2
α1
α2α3
-α1
ω ω1 ω2
2005-10-182005-10-18 1313(c) 2005 V. Guruprasad. All rights reserved.(c) 2005 V. Guruprasad. All rights reserved.
MILCOM 2005 (SIGINT US-only)
locating applicationslocating applications
fast, precise, fast, precise, monostaticmonostatic triangulation triangulation half the round-trip delayhalf the round-trip delay simpler, faster computationsimpler, faster computation infinite range of “parallax angles”infinite range of “parallax angles”
““true stealth radar”true stealth radar” where no phones go!where no phones go! seeing = rangingseeing = ranging
infinite range ~ infinite range ~ P P ∝∝ R R-2-2
““reverse-engineered” from astrophysicsreverse-engineered” from astrophysics
2005-10-182005-10-18 1414(c) 2005 V. Guruprasad. All rights reserved.(c) 2005 V. Guruprasad. All rights reserved.
MILCOM 2005 (SIGINT US-only)
isolatingisolating
F1 F2 F3 F
F = F1 + F2 + F3
received signal:“co-channel” sources at different distances
your mission,should you accept it,
is…
2005-10-182005-10-18 1515(c) 2005 V. Guruprasad. All rights reserved.(c) 2005 V. Guruprasad. All rights reserved.
MILCOM 2005 (SIGINT US-only)
isolatingisolating
F1 F2 F3 F
F = F1 + F2 + F3
received signal:
separate the signalswithout involving
content or modulation!
“co-channel” sources at different distances
2005-10-182005-10-18 1616(c) 2005 V. Guruprasad. All rights reserved.(c) 2005 V. Guruprasad. All rights reserved.
MILCOM 2005 (SIGINT US-only)
isolatingisolating
α
α α
H
F1 F2 F3 F
F = F1 + F2 + F3
received signal:
1. spread
“co-channel” sources at different distances
2005-10-182005-10-18 1717(c) 2005 V. Guruprasad. All rights reserved.(c) 2005 V. Guruprasad. All rights reserved.
MILCOM 2005 (SIGINT US-only)
isolatingisolating
α
α α
H
G2
F1 F2 F3 F
F = F1 + F2 + F3
received signal:
2. filter
“co-channel” sources at different distances
2005-10-182005-10-18 1818(c) 2005 V. Guruprasad. All rights reserved.(c) 2005 V. Guruprasad. All rights reserved.
MILCOM 2005 (SIGINT US-only)
isolatingisolating
α
α α
H
H-1G2
F1 F2 F3 F
F = F1 + F2 + F3
received signal:
3. down-scale
“co-channel” sources at different distances
2005-10-182005-10-18 1919(c) 2005 V. Guruprasad. All rights reserved.(c) 2005 V. Guruprasad. All rights reserved.
MILCOM 2005 (SIGINT US-only)
isolatingisolating
α
α α
H
H-1G2
F1 F2 F3 F
F = F1 + F2 + F3
received signal:H-1 G2 H F ≈ F2
extracted signal:
receiver processing
“co-channel” sources at different distances
2005-10-182005-10-18 2020(c) 2005 V. Guruprasad. All rights reserved.(c) 2005 V. Guruprasad. All rights reserved.
MILCOM 2005 (SIGINT US-only)
isolating applications isolating applications
distance-based selectivitydistance-based selectivity ~ directional antennae, polarizations~ directional antennae, polarizations
orthogonal to modulationorthogonal to modulation by by physicsphysics of space of space obviates TDM, FDM, CDMAobviates TDM, FDM, CDMA raises channel capacity to Rayleigh criterionraises channel capacity to Rayleigh criterion
universal anti-jamminguniversal anti-jamming even noise sources can be isolated outeven noise sources can be isolated out
2005-10-182005-10-18 2121(c) 2005 V. Guruprasad. All rights reserved.(c) 2005 V. Guruprasad. All rights reserved.
MILCOM 2005 (SIGINT US-only)
synthesissynthesis
r1
r
α1
μwave
optional signal
H(α)
~ F1
F0
r1 r2
α1
α2α3
-α1
F1
F2
F3
2005-10-182005-10-18 2222(c) 2005 V. Guruprasad. All rights reserved.(c) 2005 V. Guruprasad. All rights reserved.
MILCOM 2005 (SIGINT US-only)
synthesissynthesis
r1
r
α2
μwave
optional signal
H(α)
~ F2
F0
r1 r2
α1
α2α3
-α1
F1
F2
F3
2005-10-182005-10-18 2323(c) 2005 V. Guruprasad. All rights reserved.(c) 2005 V. Guruprasad. All rights reserved.
MILCOM 2005 (SIGINT US-only)
synthesissynthesis
r2
r
α2
μwave
optional signal
H(α)
~ F3
F0
r1 r2
α1
α2α3
-α1
F1
F2
F3
2005-10-182005-10-18 2424(c) 2005 V. Guruprasad. All rights reserved.(c) 2005 V. Guruprasad. All rights reserved.
MILCOM 2005 (SIGINT US-only)
synthesissynthesis
r
μwave
optional signal
H(α)
tune α
tune r
F0
r1 r2
α1
α2α3
-α1
ω ω1 ω2
μwav
e so
urce
RF
optic
al
F1
F2
F3
2005-10-182005-10-18 2525(c) 2005 V. Guruprasad. All rights reserved.(c) 2005 V. Guruprasad. All rights reserved.
MILCOM 2005 (SIGINT US-only)
synthesissynthesis
precise control ~ precise control ~ rr
infinite range ~ infinite range ~ αα
scales up or downscales up or down ++αα – up– up - - αα – – downdown
and genericand generic almost any wavesalmost any waves no nonlinear mediano nonlinear media no b/w, freq. constraintsno b/w, freq. constraints
r
μwave
optional signal
H(α)
tune α
tune r
2005-10-182005-10-18 2626(c) 2005 V. Guruprasad. All rights reserved.(c) 2005 V. Guruprasad. All rights reserved.
MILCOM 2005 (SIGINT US-only)
analysisanalysis
hi-fi down-scalinghi-fi down-scaling even gamma rayseven gamma rays to to μμ-waves or -waves or RFRF
nifty analytical toolnifty analytical tool• if realizableif realizable
H(-α)
tune α
RFUV
2005-10-182005-10-18 2727(c) 2005 V. Guruprasad. All rights reserved.(c) 2005 V. Guruprasad. All rights reserved.
MILCOM 2005 (SIGINT US-only)
synthesis applicationssynthesis applications
universal wave sourcesuniversal wave sources say using GW microwave sourcessay using GW microwave sources
• to yield THz, visible, UV or even gamma raysto yield THz, visible, UV or even gamma rays modulation & coherence with powermodulation & coherence with power without lasingwithout lasing
COTS-realizableCOTS-realizable main constraint: main constraint: source phase spectrumsource phase spectrum expect better with non lasing photonic sourcesexpect better with non lasing photonic sources e.g. e.g. z = 10 with z = 10 with rr = 1 m easily using Terfenol-D = 1 m easily using Terfenol-D
2005-10-182005-10-18 2828(c) 2005 V. Guruprasad. All rights reserved.(c) 2005 V. Guruprasad. All rights reserved.
MILCOM 2005 (SIGINT US-only)
sample calculationsample 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 , where
β = 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 β possible over intervals of 1 ns ≡ 1x10-9 s using
e3E6 *1E-9 ≈ 1.0030045
Max. change possible with Terfenol-D : 1.008 – 1.012
corrected: 2005-11-09
2005-10-182005-10-18 2929(c) 2005 V. Guruprasad. All rights reserved.(c) 2005 V. Guruprasad. All rights reserved.
MILCOM 2005 (SIGINT US-only)
premisepremise
1.1. wave speed independent of frequencywave speed independent of frequency• exceptions:exceptions: dispersive media dispersive media
• realm of current research with phase & group velocitiesrealm of current research with phase & group velocities
2.2. sources of nonzero spectral spreadsources of nonzero spectral spread• likely exceptions:likely exceptions: CW carriers, lasers CW carriers, lasers
3.3. spectral decomposition is receiver’s choicespectral decomposition is receiver’s choice• exposesexposes: : usual Fourier assumptions usual Fourier assumptions
• notably in quantum mechanicsnotably in quantum mechanics
2005-10-182005-10-18 3030(c) 2005 V. Guruprasad. All rights reserved.(c) 2005 V. Guruprasad. All rights reserved.
MILCOM 2005 (SIGINT US-only)
receiver’s choicereceiver’s choice
spectral analysis or selection requires summingspectral analysis or selection requires summing summing issumming is macroscopic macroscopic receiver can changereceiver can change during summing during summing
general case is NOT Fourier decompositiongeneral case is NOT Fourier decomposition Fourier <=> absolutely zero changeFourier <=> absolutely zero change zero change cannot be verified zero change cannot be verified except byexcept by distant sources distant sources
• error error isis Hubble’s law frequency shifts Hubble’s law frequency shifts
overlooked inoverlooked in all signal processing, spectrometry, even waveletsall signal processing, spectrometry, even wavelets all of astronomy & quantum physicsall of astronomy & quantum physics
2005-10-182005-10-18 3131(c) 2005 V. Guruprasad. All rights reserved.(c) 2005 V. Guruprasad. All rights reserved.
MILCOM 2005 (SIGINT US-only)
diffractive summingdiffractive summing
lens
foca
l pl
ane
grating
detector element
time = t1
static grating corresponding to
2005-10-182005-10-18 3232(c) 2005 V. Guruprasad. All rights reserved.(c) 2005 V. Guruprasad. All rights reserved.
MILCOM 2005 (SIGINT US-only)
diffractive summingdiffractive summing
lens
foca
l pl
ane
grating
detector element
time = t2
static grating corresponding to
2005-10-182005-10-18 3333(c) 2005 V. Guruprasad. All rights reserved.(c) 2005 V. Guruprasad. All rights reserved.
MILCOM 2005 (SIGINT US-only)
diffractive summingdiffractive summing
lens
foca
l pl
ane
grating
detector element
time = t3
static grating corresponding to
2005-10-182005-10-18 3434(c) 2005 V. Guruprasad. All rights reserved.(c) 2005 V. Guruprasad. All rights reserved.
MILCOM 2005 (SIGINT US-only)
summing by unsteady receiversumming by unsteady receiver
lens
foca
l pl
ane
grating
detector element
θ
older rays (from t1)
younger rays (from t3)
instantaneous sum
2005-10-182005-10-18 3535(c) 2005 V. Guruprasad. All rights reserved.(c) 2005 V. Guruprasad. All rights reserved.
MILCOM 2005 (SIGINT US-only)
summing by unsteady receiversumming by unsteady receiver
lens
foca
l pl
ane
grating
detector element
θ
n λ = l sin θ
older rays (from t1)
younger rays (from t3)
2005-10-182005-10-18 3636(c) 2005 V. Guruprasad. All rights reserved.(c) 2005 V. Guruprasad. All rights reserved.
MILCOM 2005 (SIGINT US-only)
summing by unsteady receiversumming by unsteady receiver
lens
foca
l pl
ane
grating
detector element
θ
n dλ = dl sin θ --- --- dt dt
n λ = l sin θ
older rays (from t1)
younger rays (from t3)
2005-10-182005-10-18 3737(c) 2005 V. Guruprasad. All rights reserved.(c) 2005 V. Guruprasad. All rights reserved.
MILCOM 2005 (SIGINT US-only)
summing by unsteady receiversumming by unsteady receiver
lens
foca
l pl
ane
grating
detector element
θ
n dλ = dl sin θ --- --- dt dt
n λ = l sin θ
1 dλ = 1 dl = -β -- --- -- ---
λ dt l dtolder rays (from t1)
younger rays (from t3)
2005-10-182005-10-18 3838(c) 2005 V. Guruprasad. All rights reserved.(c) 2005 V. Guruprasad. All rights reserved.
MILCOM 2005 (SIGINT US-only)
time-varying receiver statestime-varying receiver states
time
t1
t2
t3
...stationary in an expanding or shrinking reference frame
changing receiver selection state...
2005-10-182005-10-18 3939(c) 2005 V. Guruprasad. All rights reserved.(c) 2005 V. Guruprasad. All rights reserved.
MILCOM 2005 (SIGINT US-only)
traditional receiver basistraditional receiver basis
receiver ~ spectral window of representative statesreceiver ~ spectral window of representative states a state = a Fourier component mode that can be exciteda state = a Fourier component mode that can be excited a state = mode observed if exciteda state = mode observed if excited
observation by a dot-product with statesobservation by a dot-product with states as if the states were flowing into the receiver (left)as if the states were flowing into the receiver (left)
• dot-product ≡ instant-by-instant product (right)dot-product ≡ instant-by-instant product (right)
spec
tral
w
indo
w
rece
iver
st
ates
incoming signal
applied states
2005-10-182005-10-18 4040(c) 2005 V. Guruprasad. All rights reserved.(c) 2005 V. Guruprasad. All rights reserved.
MILCOM 2005 (SIGINT US-only)
traditional receiver basistraditional receiver basis
receiver ~ spectral window of representative statesreceiver ~ spectral window of representative states a state = a Fourier component mode that can be exciteda state = a Fourier component mode that can be excited a state = mode observed if exciteda state = mode observed if excited
observation by a dot-product with statesobservation by a dot-product with states as if the states were flowing into the receiver (left)as if the states were flowing into the receiver (left)
• dot-product ≡ instant-by-instant product (right)dot-product ≡ instant-by-instant product (right)
spec
tral
w
indo
w
rece
iver
st
ates
(inverted)
incoming signal
applied states
2005-10-182005-10-18 4141(c) 2005 V. Guruprasad. All rights reserved.(c) 2005 V. Guruprasad. All rights reserved.
MILCOM 2005 (SIGINT US-only)
evolving receiver basisevolving receiver basis
spec
tral
w
indo
w
rece
iver
st
ates
incoming signal
applied states
time
when receiver window itself slideswhen receiver window itself slides relative to world frequency framerelative to world frequency frame
• incoming sinusoids appear expandingincoming sinusoids appear expanding• own states appear steadyown states appear steady
2005-10-182005-10-18 4242(c) 2005 V. Guruprasad. All rights reserved.(c) 2005 V. Guruprasad. All rights reserved.
MILCOM 2005 (SIGINT US-only)
evolving receiver basisevolving receiver basis
when receiver window itself slideswhen receiver window itself slides relative to world frequency framerelative to world frequency frame
• incoming sinusoids appear expandingincoming sinusoids appear expanding• own states appear steadyown states appear steady
receiver states shorten in world framereceiver states shorten in world frame• all states ~ same function (exponential all states ~ same function (exponential λλ) ~ in world frame) ~ in world frame• position in window identifies stateposition in window identifies state
spec
tral
w
indo
w
rece
iver
st
ates
incoming signal
applied states
time
spec
tral
w
indo
w
incoming wavesapplied states
time
?
2005-10-182005-10-18 4343(c) 2005 V. Guruprasad. All rights reserved.(c) 2005 V. Guruprasad. All rights reserved.
MILCOM 2005 (SIGINT US-only)
evolving receiver basisevolving receiver basis
Dot-product selects time-varying world waveDot-product selects time-varying world wave receiver states ~ exponential-receiver states ~ exponential-λλ in world framein world frame dot-product ≡ instant-by-instant productdot-product ≡ instant-by-instant product
• vanishes for sinusoid (broken line)vanishes for sinusoid (broken line)• maximum for similar wave of same starting maximum for similar wave of same starting λλ
received component
spec
tral
w
indo
w
2005-10-182005-10-18 4444(c) 2005 V. Guruprasad. All rights reserved.(c) 2005 V. Guruprasad. All rights reserved.
MILCOM 2005 (SIGINT US-only)
evolving receiver basisevolving receiver basis
received component
spec
tral
w
indo
w
Dot-product selects time-varying world waveDot-product selects time-varying world wave receiver states ~ exponential-receiver states ~ exponential-λλ in world framein world frame dot-product ≡ instant-by-instant productdot-product ≡ instant-by-instant product
• vanishes for sinusoid (broken line)vanishes for sinusoid (broken line)• maximum for similar wave of same starting maximum for similar wave of same starting λλ
2005-10-182005-10-18 4545(c) 2005 V. Guruprasad. All rights reserved.(c) 2005 V. Guruprasad. All rights reserved.
MILCOM 2005 (SIGINT US-only)
evolving receiver basisevolving receiver basis
received component
spec
tral
w
indo
w
Dot-product selects time-varying world waveDot-product selects time-varying world wave receiver states ~ exponential-receiver states ~ exponential-λλ in world framein world frame dot-product ≡ instant-by-instant productdot-product ≡ instant-by-instant product
• vanishes for sinusoid (broken line)vanishes for sinusoid (broken line)• maximum for similar wave of same starting maximum for similar wave of same starting λλ
2005-10-182005-10-18 4646(c) 2005 V. Guruprasad. All rights reserved.(c) 2005 V. Guruprasad. All rights reserved.
MILCOM 2005 (SIGINT US-only)
evolving receiver basisevolving receiver basis
when receiver window itself slideswhen receiver window itself slides selects exponential-selects exponential-λλ wave components from world wave components from world
selected wave components bear distanceselected wave components bear distance λλ ∝∝ r r or or λλ ∝ ∝ r r -1-1
already well known in cosmology, thanks to…already well known in cosmology, thanks to…
spec
tral
w
indo
w
rece
iver
st
ates
incoming signal
applied states
time
spec
tral
w
indo
w
selected wavesapplied states
time
2005-10-182005-10-18 4747(c) 2005 V. Guruprasad. All rights reserved.(c) 2005 V. Guruprasad. All rights reserved.
MILCOM 2005 (SIGINT US-only)
Leonard ParkerLeonard Parker
Ph.D. thesis, Yale, ca. 1966Ph.D. thesis, Yale, ca. 1966 particle wavefunctions in an expanding universeparticle wavefunctions in an expanding universe leonard @ uwm . eduleonard @ uwm . edu
But what do these eigenfunctions REALLY represent?But what do these eigenfunctions REALLY represent? in their present incarnation as in their present incarnation as receiver statesreceiver states ? ?
2005-10-182005-10-18 4848(c) 2005 V. Guruprasad. All rights reserved.(c) 2005 V. Guruprasad. All rights reserved.
MILCOM 2005 (SIGINT US-only)
spectral phase gradientsspectral phase gradients Green’s function theoryGreen’s function theory
source = collection of radiating pointssource = collection of radiating points each radiating point ~ delta functioneach radiating point ~ delta function delta ~ same starting phasesdelta ~ same starting phases
consider their wave-vectorsconsider their wave-vectors
slopes ∝ distance
2005-10-182005-10-18 4949(c) 2005 V. Guruprasad. All rights reserved.(c) 2005 V. Guruprasad. All rights reserved.
MILCOM 2005 (SIGINT US-only)
spectral phase gradientsspectral phase gradients
∆φ = ∆(k r – ω t) = r ∆k + k ∆r – ∆(ω t)
signal partspace part
2005-10-182005-10-18 5050(c) 2005 V. Guruprasad. All rights reserved.(c) 2005 V. Guruprasad. All rights reserved.
MILCOM 2005 (SIGINT US-only)
spectral phase gradientsspectral phase gradients
∆φ = ∆(k r – ω t) = r ∆k + k ∆r – ∆(ω t)
k ∆r ~ holography, SAR, interferometry
signal partspace part
2005-10-182005-10-18 5151(c) 2005 V. Guruprasad. All rights reserved.(c) 2005 V. Guruprasad. All rights reserved.
MILCOM 2005 (SIGINT US-only)
spectral phase gradientsspectral phase gradients
∆φ = ∆(k r – ω t) = r ∆k + k ∆r – ∆(ω t)
∆φ = r ∆k
signal partspace part
2005-10-182005-10-18 5252(c) 2005 V. Guruprasad. All rights reserved.(c) 2005 V. Guruprasad. All rights reserved.
MILCOM 2005 (SIGINT US-only)
spectral phase gradientsspectral phase gradients
∆φ = ∆(k r – ω t) = r ∆k + k ∆r – ∆(ω t)
∆φ = r ∆k
∆ω = dφ/dt = r dk/dt
signal partspace part
2005-10-182005-10-18 5353(c) 2005 V. Guruprasad. All rights reserved.(c) 2005 V. Guruprasad. All rights reserved.
MILCOM 2005 (SIGINT US-only)
spectral phase gradientsspectral phase gradients
∆φ = ∆(k r – ω t) = r ∆k + k ∆r – ∆(ω t)
∆φ = r ∆k
∆ω = dφ/dt = r dk/dt
z ≡ ∆ω/ω = β r / c = α r
signal partspace part
2005-10-182005-10-18 5454(c) 2005 V. Guruprasad. All rights reserved.(c) 2005 V. Guruprasad. All rights reserved.
MILCOM 2005 (SIGINT US-only)
spectral phase gradientsspectral phase gradients signal part propagates envelopesignal part propagates envelope
so the slopes should be movingso the slopes should be moving
but it averages out !but it averages out !∆φ = ∆(k r – ω t) = r ∆k + k ∆r – ∆(ω t)
signal partspace part
z ≡ ∆ω/ω = β r / c = α r
2005-10-182005-10-18 5555(c) 2005 V. Guruprasad. All rights reserved.(c) 2005 V. Guruprasad. All rights reserved.
MILCOM 2005 (SIGINT US-only)
receiver’s choice (revisited)receiver’s choice (revisited) To summarize, the receiver statesTo summarize, the receiver states
are macroscopicare macroscopic therefore therefore more than likelymore than likely non stationary non stationary in general, select “Parker components”in general, select “Parker components”
• having (source distance ~ frequency) correlationhaving (source distance ~ frequency) correlation
Parker selectionsParker selections in absence of dispersion, ~ phase gradientsin absence of dispersion, ~ phase gradients fully classical, macroscopic, mundanefully classical, macroscopic, mundane
Represent space-part onlyRepresent space-part only static modes of source ~ Planck’s quantizationstatic modes of source ~ Planck’s quantization eliminates travelling pure-tones problemeliminates travelling pure-tones problem
• of photoelectric theoryof photoelectric theory
2005-10-182005-10-18 5656(c) 2005 V. Guruprasad. All rights reserved.(c) 2005 V. Guruprasad. All rights reserved.
MILCOM 2005 (SIGINT US-only)
empirical supportempirical support Hubble redshifts & “acceleration”Hubble redshifts & “acceleration”
predicted in 1995-1996 within IBMpredicted in 1995-1996 within IBM mundane resolution of 95% of estimated universemundane resolution of 95% of estimated universe
• in terms of the “baryonic” 5%in terms of the “baryonic” 5%
““Pioneer anomaly”Pioneer anomaly” also anticipated months before NASA disclosurealso anticipated months before NASA disclosure only explanation accounting for only explanation accounting for all all “features” “features”
2/32/3rdrd of lunar recession of lunar recession finally resolves oceanic friction mismatchfinally resolves oceanic friction mismatch
geological & fossil data, GPS stations datageological & fossil data, GPS stations data finally resolves “expanding earth” mysteryfinally resolves “expanding earth” mystery
no contradictory observations on any scaleno contradictory observations on any scale
all f
rom
the
unc
orre
cted
natu
ral p
last
icity
of
solid
s un
der
tidal
+ (
grav
itatio
nal,
cent
rifug
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stre
sses
2005-10-182005-10-18 5757(c) 2005 V. Guruprasad. All rights reserved.(c) 2005 V. Guruprasad. All rights reserved.
MILCOM 2005 (SIGINT US-only)
e.g. calibration in astronomy…e.g. calibration in astronomy…
calibration uses distant sourcescalibration uses distant sources colours, redshifts known from groundcolours, redshifts known from ground uses multiple referentsuses multiple referents adjusts adjusts slope slope & & curvaturecurvature
assumes relativistic redshift formulaassumes relativistic redshift formula non linear in non linear in rr
2005-10-182005-10-18 5858(c) 2005 V. Guruprasad. All rights reserved.(c) 2005 V. Guruprasad. All rights reserved.
MILCOM 2005 (SIGINT US-only)
and its subtle fallacyand its subtle fallacy redshifts are redshifts are notnot non linear non linear
pointed out by Alan Sandage among otherspointed out by Alan Sandage among others• linearity holds Local Group to SNe Ialinearity holds Local Group to SNe Ia• Pioneer anomaly fits linearly (several authors)Pioneer anomaly fits linearly (several authors)
linearity linearity ≡≡ acceleration in relativistic view acceleration in relativistic view• known by “flatness”, “quiescence”, etc. problemsknown by “flatness”, “quiescence”, etc. problems
linearity => linearity => only slope is independent!only slope is independent! calibration calibration copies incopies in ground based value of ground based value of HH00 questions high convergence in questions high convergence in HH0 0 latelylately
• even without my theoryeven without my theory
2005-10-182005-10-18 5959(c) 2005 V. Guruprasad. All rights reserved.(c) 2005 V. Guruprasad. All rights reserved.
MILCOM 2005 (SIGINT US-only)
resultsresults
as of 2001.9.11as of 2001.9.11 Refined hunch of “receiver’s choice”Refined hunch of “receiver’s choice” Matlab (Octave) validation with Matlab (Octave) validation with .wav.wav files files
as of IEEE WCNC (March) 2005as of IEEE WCNC (March) 2005 precise identification of mechanism (2004)precise identification of mechanism (2004) Java simulator – signal isolationJava simulator – signal isolation
• online examples ~ including FMonline examples ~ including FM• unjamming total destructive interference (demo’d)unjamming total destructive interference (demo’d)
2005-10-182005-10-18 6060(c) 2005 V. Guruprasad. All rights reserved.(c) 2005 V. Guruprasad. All rights reserved.
MILCOM 2005 (SIGINT US-only)
new worknew work accuracy & capability calculationsaccuracy & capability calculations
differential resolution (paper)differential resolution (paper)
major simplificationmajor simplification reduced to macroscopic bulk propertyreduced to macroscopic bulk property robust cascadingrobust cascading easier to implement, incorporate, testeasier to implement, incorporate, test
synthesis applications theorysynthesis applications theory
broad US & PCT patents filedbroad US & PCT patents filed
2005-10-182005-10-18 6161(c) 2005 V. Guruprasad. All rights reserved.(c) 2005 V. Guruprasad. All rights reserved.
MILCOM 2005 (SIGINT US-only)
current effortscurrent efforts
seeking funding, collaboration, early licensingseeking funding, collaboration, early licensing for prototypesfor prototypes for testsfor tests
seeking independent validationsseeking independent validations especially since this is “new physics”especially since this is “new physics”
• (& puts 95% of our universe at risk!)(& puts 95% of our universe at risk!)
still dark in the tunnel...still dark in the tunnel... all thought & no real test!all thought & no real test!
2005-10-182005-10-18 6262(c) 2005 V. Guruprasad. All rights reserved.(c) 2005 V. Guruprasad. All rights reserved.
MILCOM 2005 (SIGINT US-only)
acknowledgementsacknowledgements Bruce G. Elmegreen, IBM ResearchBruce G. Elmegreen, IBM Research
guidance in astrophysics researchguidance in astrophysics research early reviews & pointers, test ideasearly reviews & pointers, test ideas prompted “prediction” of Pioneer anomalyprompted “prediction” of Pioneer anomaly
• 2 months before NASA/JPL publication2 months before NASA/JPL publication
Paul S. WessonPaul S. Wesson privately confirming status of “expanding earth”privately confirming status of “expanding earth”
• (MS thesis, under Sir Jeffreys)(MS thesis, under Sir Jeffreys)
S. Eugene Poteat, President AFIO,S. Eugene Poteat, President AFIO, for mandating this paper & presentation...for mandating this paper & presentation...