Detection
•Functions and parameters contained in
this package:
In[1]:=
Out[1]//DisplayForm=
•Package functions and their basic documentation
along with simple examples
•BinaryDetectorOptimalM
In[2]:=
In[3]:=
Out[3]=
In[4]:=
Out[4]=
•BinaryDetectorProbabilityFunction
In[5]:=
Out[5]=
•BinaryDetectorSinglePulsePfa
In[6]:=
Out[6]=
•BinaryDetector
In[7]:=
Out[7]=
•CentralMomentsToLaplaceCharacteristicFunction
In[8]:=
Out[8]=
•Central
In[9]:=
Out[9]//DisplayForm=
•CentralToNonCentral
In[10]:=
Out[10]=
In[11]:=
Out[11]=
This can be expressed in a more conventional form
by writing μ for the mean and σ for the standard deviation. We
then use an abbreviated notation for higher order central moments:
In[12]:=
Out[16]=
In[17]:=
Out[17]=
Arbitraty higher order expressions can easilly be
generated:
In[18]:=
Out[18]=
One practical purpose of this function is to transform
data taken for the moments of a distribution from one form to another. For
example the data may be from explicit measurements of the pulse-to-pulse
fluctuations of the radar cross section of a realistic target. These
data can then be used to construct the LaplaceCharacteristicFunction
for this target (using CentralMomentsToLaplaceCharacteristicFunction)
which is then used in the EdgeworthDetectionExpansion or the EdgeworthProbabilityExpansion
to construct a detection model for this target (using MakeEdgeworthDetectionExpansion
or MakeEdgeworthDetectionExpansionCode).
•ChiSquareModel
•CoherentDetector
•CoherentDetectorFunction
Usage message for CoherentDetectorFunction
•CorrelationMatrix
In[19]:=
Out[19]=
In[20]:=
Out[20]//MatrixForm=
•Cumulant
In[21]:=
Out[21]=
•DetectionModels
In[22]:=
Out[22]=
•DetectionProbabilityCalculator
In[16]:=
Out[16]=
•DetectionProbabilityReport
In[24]:=
•DetectionProbability
Coherent Detector
In[25]:=
Out[25]=
In[26]:=
Out[26]=
In[27]:=
Out[27]=
Swerling 0
In[28]:=
Out[28]=
In[29]:=
Out[29]=
In[30]:=
Out[30]=
Swerling 1
In[31]:=
Out[31]=
In[32]:=
Out[32]=
In[33]:=
Out[33]=
Swerling 2
In[34]:=
Out[34]=
In[35]:=
Out[35]=
In[36]:=
Out[36]=
Swerling 3
In[37]:=
Out[37]=
In[38]:=
Out[38]=
In[39]:=
Out[39]=
Swerling 4
In[40]:=
Out[40]=
In[41]:=
Out[41]=
In[42]:=
Out[42]=
versus snr at a value of
for a single pulse:
In[43]:=
versus snr at a value of
for a 10 pulses:
In[44]:=
•Detection
•DetectionThreshold
In[45]:=
Out[45]=
In[46]:=
Out[46]=
In[47]:=
Out[47]=
•Detectors
In[48]:=
Out[48]=
•EdgeworthCumulativeExpansion
In[49]:=
Out[49]=
In[50]:=
Out[50]=
In[51]:=
Out[51]=
•EdgeworthDetectionExpansion
In[52]:=
Out[52]=
In[53]:=
Out[53]=
In[54]:=
Out[54]=
•EdgeworthProbabilityExpansion
In[55]:=
Out[55]=
In[56]:=
Out[56]=
In[57]:=
Out[57]=
•EdgeworthTerms
In[58]:=
Out[58]=
In[59]:=
Out[59]=
•ExponentialCorrelationMatrix
In[60]:=
Out[60]//MatrixForm=
•FalseAlarmNumberToFalseAlarmProbability
In[61]:=
Out[61]=
•FalseAlarmProbability
In[62]:=
Out[62]=
In[63]:=
Out[63]=
•FalseAlarmProbabilityToFalseAlarmNumber
In[64]:=
Out[64]=
•GammaExpansion
In[65]:=
Out[65]//DisplayForm=
•GaussianCorrelationMatrix
In[66]:=
Out[66]//MatrixForm=
•GCFunction
In[67]:=
Out[67]//DisplayForm=
•GramCharlierCumulativeExpansion
In[68]:=
Out[68]=
In[69]:=
Out[69]=
In[70]:=
Out[70]=
•GramCharlierDetectionExpansion
In[71]:=
Out[71]=
In[72]:=
Out[72]=
In[73]:=
Out[73]=
•GramCharlierFunction
In[74]:=
Out[74]=
In[75]:=
Out[75]=
In[76]:=
Out[76]=
•GramCharlierProbabilityExpansion
In[77]:=
Out[77]=
In[78]:=
Out[78]=
In[79]:=
Out[79]=
•LaplaceCharacteristicFunction
In[80]:=
Out[80]=
In[81]:=
Out[81]=
•LinearDetectorFunction
Usage message for LinearDetectorFunction
•MakeEdgeworthDetectionExpansionCode
In[82]:=
•MakeEdgeworthDetectionExpansion
In[88]:=
Out[88]=
In[89]:=
Out[89]=
•MarcumModel
•Models
In[90]:=
Out[90]//DisplayForm=
•MomentCentral
•MomentFunction
In[91]:=
Out[91]//DisplayForm=
•MomentMethod
The
central moment of a probability distribution of one varialbe
is
where μ is the mean of the distribution.
The
noncentral moment of a probability distribution of one varialbe
is
.
In[92]:=
Out[92]//DisplayForm=
•MomentNonCentral
•NonCentralMomentsToLaplaceCharacteristicFunction
In[93]:=
Out[93]=
•NonCentral
•NonCentralToCentral
In[94]:=
Out[94]=
In[95]:=
Out[95]=
This can be expressed in a more concisely using an
abbreviated notation for higher order central moments: .
In[96]:=
Out[99]=
In[100]:=
Out[100]=
Arbitraty higher order expressions can easilly be
generated:
In[101]:=
Out[101]=
As with the function CentralToNonCentral, one practical
purpose of this function is to transform data taken for the moments
of a distribution from one form to another. For example
the data may be from explicit measurements of the pulse-to-pulse
fluctuations of the radar cross section of a realistic target. These
data can then be used to construct the LaplaceCharacteristicFunction
for this target (using CentralMomentsToLaplaceCharacteristicFunction)
which is then used in the EdgeworthDetectionExpansion or the EdgeworthProbabilityExpansion
to construct a detection model for this target (using MakeEdgeworthDetectionExpansion
or MakeEdgeworthDetectionExpansionCode).
•NonFluctuatingModel
•PositiveIntegerOrExpressionQ
Usage message for PositiveIntegerOrExpressionQ
•PositiveOrExpressionQ
Usage message for PositiveOrExpressionQ
•ProbabilityOfDetection
Usage message for ProbabilityOfDetection
•ProbabilityOfFalseAlarm
Usage message for ProbabilityOfFalseAlarm
•ProbabilityOrExpressionQ
Usage message for ProbabilityOrExpressionQ
•ProbabilityQ
In[102]:=
Out[102]=
In[103]:=
Out[103]=
•ProbabilityQWithMessage
Usage message for ProbabilityQWithMessage
•PureSymbolOrExpressionQ
Usage message for PureSymbolOrExpressionQ
•RiceModel
•SemiInvariant
In[104]:=
Out[104]=
In[105]:=
Out[105]=
•SignalToNoiseReport
In[106]:=
In[107]:=
Out[107]=
•SignalToNoise
In[108]:=
Out[108]=
In[109]:=
Out[109]=
In[110]:=
Out[110]=
In[111]:=
Out[111]=
In[112]:=
Out[112]=
In[113]:=
Out[113]=
In[114]:=
Out[114]=
•SquareLawDetectorFunction
In[135]:=
Out[135]=
•SquareLawDetector
•SquareLawMixedDetector
•Swerling0
•Swerling1
•Swerling2
•Swerling3
•Swerling4
•Swerling5
•SwerlingCompute
•SwerlingModel0
•SwerlingModel1
•SwerlingModel2
•SwerlingModel3
•SwerlingModel4
•SwerlingModel5
|