I'm stuck with an extremely difficult numerical analysis problem and all help will be much appreciated.
Heres the question:
In certain signal detection problems (eg, radar or sonar) the probability of false alarm (FA) (ie of saying that a certain signal is present in the data when it actually is not) is given by:
.........∞
pFA = ∫ _______1_______x^p/2-1 e-x/2 dx
.........η ...Γ(p/2) 2^p/2
Where η is called the detection threshold. If p is an even number, it can be shown that reduces to the finite series:
..........................(p/2)-1
pFA = e^(-1/2 η) ... Σ ...... _1_..(_η_) ^k
...........................k=0 .......k! .... 2
P.S
. are used to align the values correctly
The detection threshold η is a very important design parameter in signal detectors. Often it is desired to specify an acceptable value for pFA (where 0 < pFA <1), and then it is necessary to solve nonlinear equation for η. Let p = 6. Use the bisection method to find η for:
a) pFA = 0.001
b) pFA = 0.01
c) pFA = 0.1
Instructions on how problem was solved will be appreciated as well so I can undertand what was done
Heres the question:
In certain signal detection problems (eg, radar or sonar) the probability of false alarm (FA) (ie of saying that a certain signal is present in the data when it actually is not) is given by:
.........∞
pFA = ∫ _______1_______x^p/2-1 e-x/2 dx
.........η ...Γ(p/2) 2^p/2
Where η is called the detection threshold. If p is an even number, it can be shown that reduces to the finite series:
..........................(p/2)-1
pFA = e^(-1/2 η) ... Σ ...... _1_..(_η_) ^k
...........................k=0 .......k! .... 2
P.S
. are used to align the values correctly
The detection threshold η is a very important design parameter in signal detectors. Often it is desired to specify an acceptable value for pFA (where 0 < pFA <1), and then it is necessary to solve nonlinear equation for η. Let p = 6. Use the bisection method to find η for:
a) pFA = 0.001
b) pFA = 0.01
c) pFA = 0.1
Instructions on how problem was solved will be appreciated as well so I can undertand what was done