Critical review on sampled-data systems

A MAXIMUM LIKELIHOOD RECEIVER FOR UNKNOWN PHASE

by John P. Flight and Ed Prism

 
 

 

Abstract
In completely remote deep-sea locations in mere temperature zones, the noise from frequencies greater than 200 Hz depends primarily on the sea and wind state.
The total acoustic power available at the difference frequency can be calculated.
Nonlinear interaction between spherical waves and that between cylindrical waves has been considered by many authors. These processes may be summarized by defining two modulation operators which will relate the input modulation signal to the modulated output in each case.

 

 
 

1- Introduction
For purposes herein the following definition of a signal is employed:
the variation through time of any significant physical quantity occurring in a useful device or system. A system in the engineering sense may be defined as any complete instrumentality which performs a specified task.
In practice, many of the signals, systems, and filters of interest satisfy the narrowband assumption. This means that the frequency content for signals, or frequency response for filters is confined to a relative narrow region around a carrier or center frequency.

Four main mathematical ideas have been developed to characterize time series:
Steady states, oscillations, chaos, and noise. A signal is, of course, a function of some parameter. When we write f(t), we mean that we have the function of parameter t. In mathematical terms, the signal f(t) is defined by giving its domain of definition (the set of values that t takes) and its range (the set of values that f(t) takes). For continuous automation of our optimization procedure, we replace the parameter-adjusting potentiometers with integrators. Positive or negative integrator inputs will respectively decrease or increase parameter values; for zero input, each integrator will hold the last parameter value.

2-A method of transmitting the data in low frequency after analog processing
The field of acoustics, viewed broadly, deals with mechanical waves at all frequencies in all substances. Significant properties associated with noise are the absence of periodic components, fairly uniform distribution of energy over a range of frequencies, and fairly constant value of power averaged over a time interval long enough to include many oscillations. A single intoned sound is meaningless in the sense of a musical investigation when, after onset or any other change it becomes stationary, or reaches a value which remains unchanged in time. A noise may consist of a single pure tone or it may contain two or more component tones.
If it contains a very large number of component tones evenly distributed over a certain frequency band the tones may be so close together as to be virtually unresolvable. However, nonlinear effects associated with acoustic waves have interested investigaters in the field of acoustics over a long period of time.
Obviously much of the discussion will also apply to clouds of air bubbles.

 
 

3-Solution of the basic equations
Speech as an acoustic process can be defined as a continuously changing structure of waves, comprising all frequencies and amplitudes over a certain frequency spectrum. (Among the more than 20.000 known species of fish, it is now clear that a large percentage , parhaps even a majority of the species are capable of producing sounds).

The essential elements in speech communication comprise a message sequence, individuals A and B, and a transmission system. The main difficulty in practice is to achieve a constant 90 degrees phase shift over the spectrum of the modulating input.
The most common application of modulation is in the transmission of information over long distances. The corresponding autocorrelation function is a delta function; the power of such a random process is theoretically infinite. In general, we resort to direct simulation, and especially to Monte-Carlo techniques, when analytical methods fail.

4-Derivation of routing coefficients
The building up of the complex sound, its becoming, is of significance aesthetically; the end product of the completely built-up sound is less interesting. Architectical forms may be lines, surfaces, or volumes, but they must always posess the dimension of time, which signifies movement – and life.
The usual rotation of air currents in our northern hemisphere is from left to right hand, while that in the southern is from right to left. The information is contained in the changes which take place during the period of our observation, as mentioned before. Both pure tone and speech audiometers are in general use for this purpose.

 
 


5- Simulation One

“Nun sind aber die toene reihenmaesig gruppiert. Es gibt zwei moeglichkeiten, vorgegebene funktionen in reihen nach ebenfalls vorgegebenen funktionen mittels analogrechner zu entwickeln. Wir schraenken das existenzbereich der signale nunmehr auf den zeitabschnitt zwischen t = 0 und t = T ein, verlangen also, dass F(t) ausserhalb dieses abschnitts identisch verschwindet. Die mindest lautstaerke soll dabei ueber dem stoergeraeusch des wohnraumes liegen”.

6-Model verification
Flow noise is a general term encompassing all those phenomena in which unsteady flow fields induce pressure fluctuations. The fluctuations may be harmonic in time, as in the field of a periodic flow, or entirely random in character.
Such a function is called a circle map. In invertable circle maps, for all parameter values inside the Arnold tongue corresponding to N:M phase-locking, all initial conditions asymptotically approach a stable N:M phase-locking pattern. The integrator drift error is, then, usually appreciable only in instrumentation applications requiring long integration times. Thus if its motion were registered over a sufficiently long period it would be seen as rhythmic. The aural effect of the electronic switch varies according to the original signal sources and the frequency of alteration.


 
 

7- Simulation Two
“Das entworfene programm ist nun auf dem programmfeld gesteckt, es wird nun der weitere ablauf der analogrechnung betrachtet. In den ersten 9 perioden nimmt die vieldeutigkeit kontinuierlich zu, die anzahl der verwendete typen jedoch nimmt symmetrisch zu und ab. Kurve 3 ist in der umgebung des arbeitspunktes (J-po) wesentlich steiler als 45 grad , d.h. das ohr ist im adaptierten zustand wesentlich empfindlicher gegen schnelle aenderungen als im ausgeruhten zustand. Die schalterstellung entspricht dem betriebszustand ‘stop’”.

8-Methods of analysis
The most important property of the bladder fish is their ability to scatter sound effectively, enabling us to make echo records and thus study them. This remark will be used in the explanation of the doppler effect in a later chapter. We should remind the reader that scaling changes not only distort the signal but also shift it.
When we take into accound the effects that messages have in a system, we enter the realm of control theory.


 
 

9- Simulation Three
“Trotz der musikalischen spekulationen, die ich vor dieser praktischen auseinandersetzung mit den moeglichkeiten der elektronischen klangerzeugung anstellte, war meine erste spontane emfindung das angesprochensein eines spieltriebs, der stets bei der verbindung von kuenstlerischen mit technischen elementen in mir ensteht. In unseren bisherigen betrachtungen traten benennbare und abstrahierbare merkmale der empfindungen nur in der metasprache des externen beobachters auf. Die verbundwahrscheinlichkeit wird dann gleich dem produkt der sende- und empfangsseitigen symbolwahrscheinlichkeiten.
Signale sind also nicht nur in der zeit- b.w. frequenzkoordinate quantisierbar, sondern auch in ihrer energetischen koordinate”.

10- Simulation Four
“Zu den regelmaessig anfallenden aufgaben des studio fuer elektronische musik gehoert die betriebsmaesige herstellung von hoerspielgeraeusche. In der regel liegen an einem integrierer beliebige anfangswerte und mehrere eingangsgroessen an. Gegeben ist ein signal y(t), das sowohl deterministischer als auch stochastischer natur sein kann.
Wichtig bleibt auch, dass neue zeichen einen hohen grad an sofortiger verstaendlichkeit besitzen und nicht etwas ganz anderes meinen, als sie vom bild her zu vermitteln scheinen. Ueber solche aeusseren harmonischen prozesse hinaus waltet, wie die beigefuegt grafik ausweist, ein seht viel differenzierter strukturplan”.

 
 

Grafik 1:

 
 

11-Electrical-analog system
Recovery of the information contained in modulated waves is called detection or demodulation. The high noise levels may also create disturbances in nearby communities. If we examine the intoned sound of unchanged pitch and loudness more carefully, we see an inner modulation even without the addition of a color change.
Each of the thirty bands has the same number of thirty shades, equalling nine hundred color shades. The most interesting circumstance is that the dimensions of the complete work were not accidental – the time value may also be traced to the symbol of the circle.
This distribution of ions gives sphalerite a peculiar and very useful electrical polarity.

Linear-model analysis of the phase locked loop does not give a complete understanding of the lock-on time of the loop, particularly when initial separation of the signal from loop center frequency is greater than 1 radian. Small loops are most often used for direction finding and for eliminating manmade noise or strong local interfering signals.
We know that the time ambiguity function Rm(t) often has the same shape as the output of a matched filter to the emitted signal m(t). These results are very interesting.

12-Components-of-flow approach
Analogous correction schemes also permit computation of three direction cosines cos alpha, cos beta, cos gamma for three-dimensional coordinate transformations. The sun, the weather, the wind, and all the materials involved in design are really something immense and, to be fully appreciated, require this kind of approach.

 
 

Figure 2: transformation of volume through illumination

 
 


Summary

The engineering procedures and calculations presented in this section can be used in analyzing and solving noise problems caused by interference of jet aircraft noise with speech communication and performance of work in administrative type facilities.
The whole structure is articulated on quantities of joints that never can be absolutely rigid, and insure to the whole work a great suppleness.

 
 

 

Sept 18, 1957