Fundamentals of electronic equipment computer aided design
Fundamentals
of electronic equipment computer aided design
1. Detection theory and signal detection
is a carrier of new information for the observer.
Presence of it in the input process causes statically characteristics change of
this process. It can be change of average value (shift parameter), dispersion
change (scale parameter), change of a correlation function (frequency spectrum
of a power), change of phase distribution (time delay) etc. in general case it
is possible to say that the presence of a signal leads to the change of
multidirectional distribution of signal mixtures and interferences probabilities.of
signals at a time of interference action is one of the fundamental tasks in
theory signal processing. The mixture of signal and interferences on the input
of the received device I general case is a random process. In case of signal
absence it is a process with definite statically characteristics (values of
probability distribution, correlation function). In most cases random process
is known to be stationary and ergodic.
In digital systems of signal processing random
processes are discretized in time, that means that analogue-digitizer (analogue-digital converter)
registries the realization process
values through definite intervals of discretization Δt.of
registrations make the sequence of random values
sequence can be written in such a way:
and be called a sample.sample of a random process
is multidetectional random value and is characterized by multidetectional
distribution of probability function
The result of digital experiment over random
process X (t) is a registration of series n coordinate values of its definite
realization
is called random process sample
realization.statement of task of signal detection in such that relatively to a
sample realization two hypothesis are advanced: hypothesis H0 -
realization of sample contains only interference; alternative hypothesis H1
- realization of sample contains interference and signal.
During making decision about choice between H0
and H1two types of errors are possible. First of
all there could be errors connected with correct zero hypothesis deviation H0.
Such error is called an
error of the first type. Its probability is defined by the letter α.
Secondly, it is possible to recognize alternative H1 incorrect when
it will happen. It will be the error of
the second order. Its probability is defined by letter β.
γ(x1… xn) H
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γ = 0
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γ = 1
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H0
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(1
- α)
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α
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H1
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β
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(1
- β)
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In theory of signal detection the error of the
first order is called false alert, and corresponding probability α - probability of false alert. The
situation of the missing signal corresponds to the error of the second order.
The probability of signal missing β is directly connected with the
probability of correct signal detection D.
. Detectors
Classification of signal detector
Parametrical
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Adaptive
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Non
parametrical
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are known
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- is unknown, - are known
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- are unknown
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detector is a device that recovers information of
interest contained in a modulated wave. The term dates from the early days of
radio when all transmissions were in Morse code, and it was only necessary to
detect the presence (or absence) of a radio wave using a device such as a
coherer without necessarily making it audible.the study of course fundamentals
of electronic equipment computer aided design we observe three types of
detectors such as parametric, adaptive and nonparametric detectors, which have
differences in their work.) Parametric detector
the parametric detector:
α
- Var, β - Var - is no stability meaningsparametric detector contains a coupled
film sensor stripe and an excitation conductor which, electrically insulated
from each other, cross at right angles. A sensor stripe consists of a pair of
super positioned stripes which are separated by a thin nonmagnetic layer. A
high frequency excitation current in the conductor produces an inductive output
signal in the sensor stripe. The waveform of this periodic signal is responsive
to domains proximate to the sensor/conductor crossover area.parametric detector
comprising a coupled film sensor strip, and excitation means interacting over a
limited area with said stripe wherein the passage of a periodically varying
current in said excitation means produces a similarly periodic inductive output
signal from said stripe having a waveform responsive to the present of a domain
proximal to said limited area.) Adaptive Detector
For the adaptive detector:
α - is
constant, β - Var - no stability meanings
3. Let’s define the
detection abilities of different detector’s types
signal detector information
We must choose the detector which shows the
smallest probability of errors with our given data.to my number in the list of
our group (N=10), I have such values:- number of ranks (for non-parametric
detector)- loss from a false alert= 5= 0.1
R= C1α
+ (1-C1)β
Text of a program:
DIM x(200), y(200)
ps = 1: s = 5: v = 2: ai = 0: bi = 0: mx = 2: my
= 10: ax = 200: m = 5: c1 = 0.1:i = 1 TO 200(i) = SQR (-2 * ps * LOG(RND)) *
COS (6.28 * RND)i > 100 THEN x(i) = x(i) + sx(i) > v THEN y(i) = 1 ELSE
y(i) = 0ii = 1 TO 200i < 100 AND y(i) = 1 THEN ai = ai + 1 / 100i > 100
AND y(i) < 1 THEN bi = bi + 1 / 100i= c1 * ai + (1 - c1) * bi ai, bi, R
Adaptive
DIM x(200), y(200)= 1: s = 5: v = 2: ai = 0: bi =
0: mx = 2: my = 10: ax = 200: m = 5: c1 = 0.1:= -100: ymin = 100: k = 1.8i = 1
TO m(i) = SQR (-2 * ps * LOG(RND)) * COS (6.28 * RND)ymax < y1 (i) THEN ymax
= y1 (i)ymin > y1 (i) THEN ymin = y1 (i)i= (ymax - ymin) / 6= sm * ki = 1 TO
200(i) = SQR (-2 * ps * LOG(RND)) * COS (6.28 * RND)i > 100 THEN x(i) = x(i)
+ sx(i) > v THEN y(i) = 1 ELSE y(i) = 0ii = 1 TO 200i < 100 AND y(i) = 1
THEN ai = ai + 1 / 100i > 100 AND y(i) < 1 THEN bi = bi + 1 / 100i= c1 *
ai + (1 - c1) * biai, bi, R
my variant
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Parametrical
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Adaptive
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α
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β
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R
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α
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β
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R
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1
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0.31
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0
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0.031
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0.01
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0
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0.001
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3
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0.31
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0.01
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0.04
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0.11
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0.04
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0.047
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5
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0.02
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0.049
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0.16
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0.09
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0.097
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|
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0.04
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0.048
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Our input signal looks like
When
σ=1
When
σ=3
When
σ=5
For parametrical adder
When
σ=1
When
σ=3
When
σ=5
For adaptive adder
When
σ=1
When
σ=3
When σ=5
Our adder:
Conclusion
signal detector information
In our work we investigate three type of
detectors: parametric and adaptive for all we calculated probability of first
and second kind error and risk. Due to my data, i make the conclusion, that the
most optimal parametrical detector, because it have the smallest number of R -
risk. Of course it have great probability of the first kind error, but it is
most optimal choice between our detectors.