Note this article was updated with the new FILMS- of Patrick Botte and Dan Winter- in Jan 2017 at: www.hrv-app.com/realheartcoherence
Companion article on how itHRVe measures stress- at: www.hrv-app.com/stress.html
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itHRVe Stress Managament New HELP FILES: craniosacral-app.com/ITHRVE%20STRESS%20MANAGEMENT/manuals-2.html
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from Dan Winter - in association with lead programmer- and Sacral Cranial expert - Patrick Botte- for itHRVe project- April 4, 2016
Main link for the new app: ithrve.com
How itHRVe Measures Heart COHERENCE
--With itHRVe - you have the latest science in the measurement of Heart Coherence. We display a simpified (and limited -see below ) - single harmonic version of heart coherence measure - ANDin addition- we display the far more sophisticated and healthy harmonic inclusive- FULL SPECTRUM COHERENCE (3rd order power spectra- see below).
Below- in green and - see the third order power spectra (or FFT3) - graph of coherence in the HRV- as plotted by itHRVe. Note we plot both that graph derived directly from the HRV peak - and separately derived from the wave of blood pressure change- which itHRVe is able to separately measure and graph (see discussion also in Stress Measue with itHRVe).
Important credit here: the concept of using the THIRD ORDER FFT- to quantify (& thus smooth the measure of) INTERNAL PHASE COHERENCE-
and to compare that to the simple Single Harmonic Coherence- is thanks to Patrick Botte
With itHRVe - you can also actively compare the simpler Heart Math kind of notion- for simple 1 harmonic heart coherence (above in white)- with the more sophisticated and more truely health indicative- FULL SPECTRUM (3rd order FFT) heart coherence measure ( above in pink).
Once you know that the EKG (lo) frequencies / HRV-are actually self organizing / NEGENTROPIC - in a precise PHASE CONJUGATE IMPLOSIVE COLLAPSE ( see fractalfield.com
THEN you can perfect HEART Rejuvenation- by this new frequency equation from Dan Winter- with an entirely deeper meaning of HEART COHERENCE:
Here are the HRV frequencies- LF and HF and the MAYER WAVE- and here is the equation for perfected implosive "ORIGIN OF BIOLOGIC NEGENTROPY":
(from article www.fractalfield.com/conjugateperception ) -Also shown the Phase Conjugate HRV/Breath driven - Sacral Cranial frequencies- and the phase conjugate ADP/ATP - cellular energy key:
Heart coherence has almost mythic importance among students of spiritual science- and emotional biofeedback. And there is good reason for this.
When I originally discovered how real heart coherence is meaasured- (see image- my HeartTuner) - we oftened used the Internal Cardiac Coherence peak- not just to measure the kinesiology response- but quite literally as a lie detector.
That invention was based on my original and unique discovery that Heart Coherence could best be measured by using a second order power spectra of the heart data - called the CEPSTRUM. This was my discovery for which I was credited in the literature for inventing the concept of heart coherence. That invention- my HeartTuner was later essentially stolen by an unscrupulous programmer I hired. Fortuneately- since it is now badly overpriced- and completely obsolete- there is a more powerful replacement: itHRVe.com - which is reasonably priced. Interestingly - Heart Math Institute also took from me without acknowledging my discovery of how to do power spectra of EKG to reveal emotional coherence. I spent weeks and 2 flights to California teaching Rollin McCrarty how to take his first EKG and how to take the power spectra of it . I tried to teach them to understand heart coherence- from the day they first learned to take an EKG from me, and then they first learned to take the power spectra from an EKG from me (I can prove this- their failure to acknowledge me - demonstrates their lack of integrity).
It was approximately 1990 when HeartMath Institute paid Dan Winter - to instruct them initially how to measure heart harmonics. They contacted him requesting assitance to replicate work in his 'Alphabet of the Heart' (now at goldenmean.info/book1 ) published in the 1980's where in he showed the heart responding measureably to 'sending love': (pic)
Above- Dan Winter's actual original discovery print-out from the 1980's showing that measuring lo frequency EKG power spectra- could reveal emotional states
- a concept later stolen by Heart Math Institute - without credit to Dan Winter.
The present Heart Math Institute simple 1 harmonic concept of Heart Coherence - has serious limitations:
Note here in what I call the HEART MATH MISTAKE:
The Heart Math concept of looking for a single harmonic in the Heart HRV data to become a sine wave-- which they call coherence- can actually be an unhealthy simplification.
The true meaning of heart coherence- relates to the true measure of what makes heart harmonics indicated immune health. The proper term for that in the HRV medical literature is HARMONIC INCLUSIVENESS. Please read about the harmonic inclusive heart- as the healthy heart- in my article with Dr Irving Darik of 'Making Waves' - see: goldenmean.info/holoarchy
The concept may be simply expressed - the more DIFFERENT harmonics which your heart as an oscillator contains- the more healthy you and your immune system become. The physics of what allows a maximum number of different harmonics to exist 'non-destructively' in a single oscillator- is the real deep meaning of Heart COHERENCE.
This is what using second and (in itHRVe) third order power spectra analysis do- to reveal deep coherence. They allow us to reward a harmonic rich coherent harmonic series - in your heart- as real coherence ( instead of simply one harmonic- which is rewarded- the so called 'Heart Math Mistake').
===below - more on the history of Heart Coherence measure from Dan Winter
Evidence Fractal Phase Conjugation (harmonic inclusiveness optimized)
IS The Deep Physics of Quantum COHERENCE www.fractalfield.com/coherence
with the real history of Coherence Science..
Heart Coherence- Video Presentation from Dan Winter , Fri Sept 17, 2010
to Dr Mark Filippi - for International Conference of Coherence Conference.. ( below)
You knew that coherence is perfected by (phase conjugating - Golden Ratio) FRACTALITY (Nodes in the hologram WORK by compression perfected).
You knew that was the musical key signature of EKG and EEG - DURING coherent emotion-
which generates the (phase conjugate dielectric) of 'DNA RADIO'.
(HOW we FEEL each other... hint to Rollin and Doc at Global Coherence - those who actually understand the math and field theory of how coherence is produced - phase conjugate dielectric capacitive coupling is how your Josephson Junction transducer works.. actually can BUILD the bioactive field)
You knew all of this originally from Dan Winter- inventor of HearTuner, BlissTuner and the word HEART COHERENCE
- as used in the literature..(history of COHERENCE links below)
Best to hear the story from the "horses mouth"- see the film at www.fractalfield.com/coherence
Links for with presentation: History of Dan Winter's discovery of and original invention - measurement of Heart Coherence:
Mathematics of measuring Heart Coherence
Contrast with The HeartMath "MISTAKE"
Dan Winter- originates HEART COHERENCE-as quoted in:
"HEART COHERENCE was first described in 1992 by physicist Dan Winter" - from David Servan-Schreiber Ph.D. new book"Instinct to Heal".
This article presents the research history evidence - not only does HeartMath Institute not properly measure Heart Coherence - and mislead people into thinking that breathing at one frequency (what their Freeze Framer teaches) is Heart Coherence. But further - they have seriously mislead the world into thinking they somehow invented Heart Coherence. The irony is - that for the first 2 years after Dan Winter flew there at their expense to teach them how Heart Coherence - was measured (& how to take an EKG and analzye it) - they in fact dozens of times refused to believe (Rollin McCraty et al) that Heart COHERENCE was the correct term. THEN finally - when they saw that Dan Winter was correct - about COHERENCE in the Heart - THEY FAILED TO EVEN MENTION THE SOURCE OF THEIR TRAINING IN MEASURING and Spectrum Analyzing EKG originally. Today - they still fail to teach people that the single frequency breath taught by their FREEZE FRAMER - is neither HEART COHERENCE ( see Cepstrum measure ) NOR does it produce the HARMONIC INCLUSIVENESS (in HRV) clearly required for health. ( see goldenmean.info/dardik ). Using the OPPOSITE technique - breathing in a CADUCCEUS CASCADE of INCLUSIVE HARMONICS ( trainer at : goldenmean.info/caducceus ) DOES create measureable HEART COHERENCE - which IS measureable using the correct EKG Cepstrum - the Heart becomes a laser. AND this DOES produce harmonic inclusiveness (in Heart Rate Variability). -------------- end exerpt from www.goldenmean.info/coherence
How harmonic inclusiveness produces fractality and therefore all viability:
www.goldenmean.info/holarchy (review of Irving Dardik work)
Implications of Discovering Coherence is Perfected by Phase Conjugate Fractality:
The cause of (all centripetal self organizing forces)
gravity, perception, life force, bliss, color
Our Commercial Applications - Of Implosive (Fractal) Coherence
Film from Dan Winter above- is part of:
co·her·ence : The working definitions for coherence range from the tangible to the abstract, from the literal to the figurative, from the cosmic to the cosmetic. Our aim at this conference is to apply them to real-world issues facing people from all walks of life as we enter the era of Health 2.0. Bring your own brain!
This article Concept Creation, Coherence, and Cohesion gave us this version of it...
The conceptual schema we're exploring like these blind men touching the elephant here is how coherence can be applied to the emerging world of Health 2.0 going forward. This transcends the dry clinical and academic arguments and gets into the more raw terrain of ecomonics, memetics, epigenetics and other socially-based fields
Anatomical Coherence: Tom Myers
Perceptual Coherence: Karl Pribram
Epigenetic Coherence: Bruce Lipton
Memetic Coherence: Richard Brodie
Human Performance Coherence: Pete Egoscue (video contribution)
Energy Medicine Coherence: James Oschman (powerpoint contribution)
Cognitive Neuroscience Coherence: David Goodman (video contribution)
Cardiocybernetic Coherence: Irving Dardik
Personalized Medicine Coherence: Peter D'Adamo
Decentralized Economic Coherence: Douglas Rushkoff (video contribution)
Positive Psychology Coherence: Mihaly Csikszentmihalyi
New Cosmology Coherence: Rob Bryanton (video contribution) (author of "Imagining The 10th Dimension")
Crowd Energy Dynamics: Rick Leskowitz (Co-producer of 'The Joy of Sox' documentary) (video contribution)
Self-Regulation Coherence Stephen Elliott (creator of Coherent Breathing techniques) (video contribution)
Behavioral Coherence: Deborah Rozman, HeartMath LLC
Global Fractal Coherence: Dan Winter (video contribution)
Spiritual Development Coherence: Mark Epstein
Polyvagal Coherence: Stephen Porges
Nonlinear Dynamical Coherence: Fred Abraham*
Epistemological Coherence: Rick Paar*
Visual Logical Coherence: Marc Grossman
Neurobiological Coherence: W. Roulette Smith*
Quality Of Life Coherence: Nic Marks (video contribution)
---and speaking of coherence in the flow..
Heart Coherence / Entrainment / Empathy Training / HRV / Yogic Breath - BIOFEEDBACK for iPhone:
talk about EMBEDDING PERFECTED!
Historical background: Defining Heart Coherence
from Dan Winter- who is credited in the literature with inventing the concept of Heart Coherenc
Teaching Biological Oscillators SUSTAINABILITY -
- As we release itHRVe.com
-Breakthru in Measuring INTERNAL COHERENCE.
Coherence: Defining & Measuring, in the Heart and in All Oscillators.
this article is an extension of earlier literature review on the pioneer- HeartTuner- Dan Winter's invention, research history: see: goldenmean.info/heartjournal
New Heart (& Brain) (ECG & EEG) Coherence Biofeedback Tool Portends to Revolutionize:
1. Emotional Coherence Measurement
2. Empathy and Concensus Measurement (& Clinical Counseling)- Tantra / Marriage & Relationship Counseling / Concensus Process / Conflict Resolution - CAN 2 Hearts LINK??
3. Brain Coherence Measure to Teach A.D.D. / Addiction Remission & Meditation Success. (Internal Brain Wave COHERENCE has never before been measured )
4. Ability to Measure and Teach Move from Conceptual/Head Centered to Empathic/Open HeartCentered Emotion.
5. Life Force Measurement by the same technique-may redefine VIABILITY as 'harmonic inclusiveness' using New electrical definition of life itself.
ABOUT Dan Winter (from Implosion Group files)
(note please see Definitions of CEPSTRUM ( or below)-- it appears particularly that the lower frequency bandwidth within which the significant power densitites of the EKG exist - allow the cepstrum technique - to qunatify internal coherence - specifically quantizing the onset of phase synchrony between internal harmonic constituents.)
Summary: I have pioneered a radically new and elegant way of measuring INTERNAL or AUTO-COHERENCE in any osicallating signal. The technique involves using a second order power spectrum / Fast Fourier Transform (FFT). The second order FFT is sometimes called a SEPTRUM (note more often spelled CEPSTRUM). This might be thought of taking a POWER SPECTRA OF a POWER SPECTRA. (This is completely different than a simple inverse FFT). We may have been the first to successfully apply the use of the SEPTRUM to dynamically analyze biological signals. The radical breakthru consists in the VISIBLY OBSERVABLE fact that the AMPLITUDE of the first or primary peak of this septrum, is a real and dynamically interactive measure of INTERNAL COHERENCE.
"The power spectrum of power
spectrum (Cepstrum) reduces to the square of the convolution of
the original signal with its complex conjugate in case that signal
is complex. The Fourier transform of power spectrum reduces to
the convolution given by
F(t) = INT f(t-u) f*(u)du , where f(t) is original signal.
This function of time is *real* even when f is complex. Double power spectrum G is square of this function: G= F(t)2 and characterizes coherence"
--- Inspection alone proves that we measure coherence in this new way. When the peaks of the regular power spectra become evenly spaced (PHASE COHERENT) then the peak of the septrum-2nd order power spectra rises - MEASURING Internal or Auto COHERENCE IN A RADICALLY NEW AND ELEGANT WAY. The mathematics of this is simple: the second order power spectra treats the first order power spectra as an indepent oscillating wave - when that is ordered (coherent ) it sees that as a coherence peak in the second order display / septrum. Only if the first order power spectra has harmonic peaks in locked regular PHASE (coherence) can the second order spectra show a peak - whose amplitude more elegantly quantifies internal / auto coherence than has ever before been possible! ---
Note: this is a radical departure from the conventional mathematics which suggest in general coherence can only be quantified in the comparison of 2 separate oscillators. The COHERENCE within a single complex oscillator is sometimes called AUTO or INTERNAL COHERENCE. And to our knowledge has never before this invention been accurately measureable interactively.
By applying this to EKG and EEG - and thus MEASURING INTERNAL COHERENCE in biofeedback interactively we appear to be already revolutionizing the teaching of EMOTIONAL COHERENCE - in the Heart - and ATTENTION / BRAIN COHERENCE in EEG. ( In addition the numeric position / value of the first primary peak of the SEPTRUM gives us the VALUE of the MUSICAL KEY SIGNATURE of the Heart / Brain (or any osciallator ) instantly and interactively. Giving us another profound biofeedback tool.)
If indeed we are correct that this tool allows us to evaluate loss of internal or auto COHERENCE dynamically, the implications are profound in almost every area of physics. For example, by mesuring coherence loss in this way in DNA we would surely have a powerful tool to check on the work of genetic engineers: Letter to the UN:Genetically Modified Foods-Threaten the Physics of COHERENCE (& Ensoulment?) in DNA. Genetic engineers have been very DANGEROUSLY ignoring their responsibility to our genepol survival by ignoring the simple fact that the sustainability of DNA is undeniably it's FIELD EFFECT. Only such an INTERNAL COHERENCE measure as we propose here, can quantify this 'immortality factor' in DNA. Without this, our genepool is at risk, because the simple fatal problem of FRACTIONATION in DNA has not even before been considered by genetic engineers, simply because before this invention they had no way to measure it!.
The challenge issued here is to the mathematical community. A mathematical formalism is needed that would prove the fact discovered by inspection, that internal COHERENCE can be measured by using the SEPTRUM/CEPSTRUM.
Summarizing the challenge to the mathematical community: In effect does the MEASURING OF COHERENCE enable the biological teaching of wave sustainability?
1. A new and elegant way of measuring internal (or auto) COHERENCE could revolutionize physics in the most basic of ways - not the least of which would be the optimizing of biological sustainability in all living oscillators - since coherence is literally the difference between life and death for every wave, gene, heart, and human. (example of wave sustainability in a biological oscillator predicting longevity - in EKG : The Origin of Disease and Health Heart Waves )
2. I have found a new way to measure this coherence using the 2nd order FFT as power spectra ( sometimes called SEPTRUM, note- this is NOT an inverse FFT function).
3. Everyone who has seen this work (sample screen below) (bottom left chart)- has agreed - FROM A SCIENTIFIC VIEWPOINT IT IS VISUALLY SELF-EVIDENT THA THE AMPLITUDE OF THAT FIRST MAJOR SEPTRUM PEAK GROWS AS THE REGULAR POWER SPECTRUM BECOMES COHERENT. It stands to reason that you use the wave shape of the power spectrum to do ANOTHER power spectrum, than you will ONLY GET A PEAK IF THE INPUT WAVES ARE ORDERED OR COHERENT.
4. So this is the challenge to the math community. All that remains, is to develop a mathematical formalism (proof of sorts) that evidences mathematically, that which is already evident by inspection. Namely : THAT THE 2nd ORDER FFT in the form of POWER SPECTRUM (or SEPTRUM), IS AN ELEGANT WAY TO MEASURE COHERENCE.
5. Suggested key words for your research : Cauchy, Coherence, Septrum, Schwartzschield Inequality..
below from: December/13/2001
We have been discussing the definition of COHERENCE as it applies to the HEART, for years. Stars in these conversations have been, Rollin McCraty of Heart Math Institute, and now Andrew Junker, PhD, our HeartLink engineer and builder, from CyberLink Systems.
This note suggests a relationship between the poetic, the optical, the mathematical definitions of coherence. Further, it suggests our new technique of second order FFT / 'SEPTRUM' (frequency signature OF the frequency signature), as a powerful way to access, measure, quantify, feedback, and teach COHERENCE.
Return to Main Article on HeartTUNER "The LoveBug"
return to Sacred Geometry master index /sitemap.html
Other examples of biological COHERENCE measures:
Teaching HEAD - HEART coherence: The above SEPTRUM plot (lower left) compares the internal COHERENCE (peak AMPLITUDE) - and simulataneously PHASE ENTRAINMENT (peak X axis value / musical key ) of one persons heart (EKG in black ) with BRAIN (EEG in RED).
ABOVE comparing the relative INTERNAL-COHERENCE of right vesus left hemisphere brainwaves (EEG). (To teach cross hemispheric coherence in a new more elegant way.) The lower plot is SPETRUM - second order FFT.
In the HeartLink we use the 2nd order FFT or Frequency Signature as a radically new and radically elegant mathematical tool to quantify the INTERNAL coherence in ANY complex oscillator.
The 2nd order fft is technically called 'septrum'. As far as known my invention Heartlink is the first clinical
application of the concept. We take the REAL data output matrix of the first order fft, and use that as the input to a
2nd order fft, which is then displayed from 0 - 2 hz. The Scale being the inverse of the average distance in hz between
coherent peaks of the first order fft.
The amplitude of the first major peak of this septrum, between
.4 and 1.2 hz is the new measure of coherence. Further the numeric
value or position of this peaks is the inverse of the musical
fundamental of the EKG. (Which HeartMusic key signature becomes
the key of the voice etc. see ../heartvoice)
Supposing we were to consider the heart's distribution of voltage waves as if it were a simple light beam trying hard to become so powerful as to be worthy to be called "a laser". Then our question about measuring heart coherence becomes the same one as a laser optics physicist attempting to predict the moment at which a light beam became "coherent" enough to penentrate distances like a laser. The internal "coherence" or columnation of phases within the single beam would determine how penetrating was that beam.
So too with the heart. We know that the heart electricities effect the immune system and the environment. Therefore the more sustainable these heart "waves", the more effective in bending their environment. So we need a way to teach people to make their heart "waves" sustainable, that is: able to reach further without collapsing as waves. We provide this "heartlink" as a tool to measure this "coherence", and feed it back in such a way as to make it teachable.
The first peak of the second order FFT clearly rises animatedly as a persons heart coherence or heart harmonics rise in the first fft. The key step in realizing the technical meaning of the word coherece, in this regard, is to understand that a SINGLE wave or parameter in a technical sense, does not HAVE coherence.
Note below, in the physics literature: definition of coherence:
"Coherence--A mathematical algorithm expressing a quantitative measure of the spatial or temporal relationships between two or more parameters. Simple coherence is the ratio of the square of the absolute magnitude of the cross spectral density function between two parameters and the product of the power spectral densities for each individual parameter. (For a generalized definition of coherence, including multiple and partial coherence, see Goodman, 1965.)"
that indeed at least TWO parameters must be COMPARED to talk about coherence.
So, would could not describe the ekg as a wave as having coherence IF we think of it as a single parameter. However, if we were to consider each of the sine waves arranged in the complex series we call the frequency signature or power spectra or FFT ( of the heart voltage) , THEN we could talk about the COHERENCE BETWEEN those internal harmonics.
THIS is indeed what I believe this second order frequency plot (fft) does for the heartlink. Specifically, that the height or amplitude of the first peak of that plot, is a measure of whether those harmonics of the first FFT are evenly spaced (OR LITERALLY PHASE DISCIPLINED or coherent). What indeed is powerful here is that this technique of taking the second order FFT OF ANY OSCILLATOR , now can be understood as a way to quantify the INTERNAL harmonic COHERENCE OF ANY OSCILLATOR.
What happens practically, is that the second FFT CHECKS to see if the space or PHASE between the harmonics of the first FFT are even or disciplined. If yes, then the amplitude of the first peak of the second FFT MEASURES THAT PHASE COHERENCE.
Bob Zawada reports a mathematical precedence for the second order fft function I have applied to
1. quantifying coherence in any complex oscillator
2. quantifying interharmonic spacing (Emotional Intelligence) in EKG
(to teach emotional intelligence in biofeedback).
In the literature:
"Theory of Fourier Integrals"
researcher Cauchy works with the Fourier material on
Analytical Theory of Heat & Molecular Motion.
Cauchy,in the 1st chapter calls what I have labeled a "second order fft" a "reciprocal function of the second kind". Zawada notes that my technology "heartlink" and Emotional Intelligence measuring may indeed be the first known example of ANY real world application of this mathematics, described in 1970.
In my view, clearly this new mathematical technique I have pioneered quantifies the approach to coherence, recursion, self organization, and thus self awareness in any complex oscillator. This enables feedback loops IN GENERAL to teach self-direction/awareness/organization.
I proposed the following additional solution to cancer to Zawada today, using this technique.
Please see the discussion of cell membrance COHERENCE versus cancer:
Albert Szent Gyeorgi showed that increased molecular ordering in cellular water prevents cancer by increasing wide distribution of triplet state electrons.(Basically cheaper phone calls between sub cellular molecules to improve TIMING coordination for meitosis the heart of cancer resistance).
(his nobel prize winning work related to his book "Electronic Biology & Cancer").
What he lacked was a tool to optimize and measure the cells skill to make that water "ice-9" like.
Now we have that tool.
Jim Patterson (CLEAN ENERGY TECH INC, 14332 MONFORT,SUITE 6302,dallas,tx,75240, 214-458-7620, patterson water cell, palladium -dodec - bead etc)
showed that light scattering thru water could dependably measure whether the water had been near the body of a healer. (order increase). By using my new mathematical tool on the complex light scatter thru the water, we should clearly be able to teach that water to approach the limit condition of coherence which is the mathematical geometry of embedding perfected by phi.
from link above goldenmean.info/cepstrum
Definitions of CEPSTRUM ( a re-attangement / anagram of the letters of spectrum / spelled as septrum earlier )
return to Breakthru in Measuring INTERNAL COHERENCE.Teaching Biological Oscillators SUSTAINABILITY -
(note -- it appears particularly that the lower frequency bandwidth within which the significant power densitites of the EKG exist - allow the cepstrum technique - to qunatify internal coherence - specifically quantizing the onset of phase synchrony between internal harmonic constituents.)
The Fourier transform of the logarithm of the autospectrum. Useful for determining periodicities in the autospectrum. Additions in the cepstrum domain correspond to multiplication in the frequency domain and convolution in the time domain.
V or dB vs. s
The cepstrum is the forward Fourier transform of a spectrum. It is thus the spectrum of a spectrum, and has certain properties that make it useful in many types of signal analysis. One of its more powerful attributes is the fact that any periodicities, or repeated patterns, in a spectrum will be sensed as one or two specific components in the cepstrum. If a spectrum contains several sets of sidebands or harmonic series, they can be confusing because of overlap. But in the cepstrum, they will be separated in a way similar to the way the spectrum separates repetitive time patterns in the waveform. Gearboxes and rolling element bearing vibrations lend themselves especially well to cepstrum analysis. The cepstrum is closely related to the auto correlation function.
from - about Cepstrum
1. The term cepstrum was introduced by Bogert et al. and has come to be accepted terminology for the (note insert from dan winter - this is wrong! it is not inverse) inverse Fourier transform of the logarithm of the power spectrum of a signal. (L.R.Rabiner and R.W.Schafer, Digital Processing of Speech Signals, Prentice Hall, Englewood Cliffs, NJ, 1978)
2. In 1963, Bogert, Healy and Tukey published a paper with the unusual title "The Quefrency Analysis of Time Series for Echoes: Cepstrum, Pseudoautocovariance, Cross-Cepstrum, and Saphe Cracking."
They observed that the logarithm of the power spectrum of a signal containing an echo has an additive periodic component due to the echo, and thus the Fourier transform of the logarithm of the power spectrum should exhibit a peak at the echo delay. They called this function the cepstrum, interchanging letters in the word spectrum because "in general, we find ourselves operating on the frequency side in ways customary on the time side and vice versa."
Bogert et al. went on to define an extensive vocabulary to describe this new signal processing technique; however, only the term cepstrum has been widely used. (A.V.Oppenheim and R.W.Schafer, Discrete-Time Signal Processing, Prentice Hall, Englewood Cliffs, NJ, 1989)
3. The transformation of a signal into its cepstrum is a homomorphic transformation, and the concept of the cepstrum is a fundamental part of the theory of homomorphic systems for processing signals that have been combined by convolution. (A.V.Oppenheim and R.W.Schafer, Discrete-Time Signal Processing, Prentice Hall, Englewood Cliffs, NJ, 1989)
4. Books including the subject about cepstrum and homomorphic systems
* Discrete-Time Signal Processing, A.V.Oppenheim and R.W.Schafer, Prentice Hall
* Digital Processing of Speech Signals, L.R.Rabiner and R.W.Schafer, Prentice Hall
* Discrete-Time Processing of Speech Signals, J.R.Deller,Jr., J.G.Proakis and J.H.L.Hansen, Prentice Hall
* Seismic Applications of Homomorphic Signal Processing, J.M.Tribolet, Prentice Hall
* Onsei Singou Syori (in Japansese, Speech Signal Processing), S.Imai, Morikita Publishing
This book describes modern Cepstrum analysis technology and its applications in speech processing.
log magnitude approximation (MLA)
6. Example of the Hypersigal worksheet of power cepstrum-source of Hypersignal worksheet
7. Cepstrum Co., Ltd. is a developer of digital signal processing system/software in Japan.
Also Cepstrum is the dealer and 3rd party developer of Hypersignal in Japan.