Esteem of the power phantom
1) statistical Parameters of a stationary aleatory process:
medium valor
temporal medium
temporal medium of every sequence champion
variance
autocovarianza
spectral density of power
2) Esteem of the average :
it only represents an accurate esteem if N is a number much elevating.
3) good Appraiser :
He is an appraiser for which the probability is elevated that the esteem is next to the parameter to estimate, that is the probability density must tight and be concentrated around to the true value.
4) Polarization of one appraiser :
It is the difference between the true value to of the parameter and the expected
value of the 
esteem.
5) Variance of one appraiser :
6) medium quadratic Error of one appraiser :
7) consisting Appraiser:
He is an appraiser for which the polarization and the variance stretch both to zero to growing of the number of observations.
8) Esteem to maximum verosimiglianza:
Esteem to maximum verosimiglianza of valor medium the mx of one aleatory process
is the medium collection of samples
characterized from a variance 
and from null
polarization therefore since to growing of N the variance diminishes
it has that the medium collection of samples is one consisting
appraiser.
Esteem to maximum verosimiglianza of the variance of an aleatory process
, in case mx is not famous can be replaced in the expression from its
esteem, is had per² that the expected value of the variance champion
does not coincide with the variance for N small introducing therefore
one polarization that to scompare for N®¥ . The variance of the variance
champion is 
therefore is had that the variance
champion is a consisting esteem.
9) Esteem of the sequence of autocorrelationship of a null process to average:
draft of an appraiser consisting in how much has not been polarized and its variance stretches to zero for N®¥ .
10) Esteem of the sequence of autocorrelationship of a null process to average:
draft of an appraiser consisting in how much has not been
polarized and its variance stretches to zero for N®¥. It
is had per² that if m®N the
variance of the esteem grows remarkablly rendering same the esteem not
useful, such disadvantage is not instead present in the 
esteem.
11) Periodogramma of one sequence white woman:
it is a polarized esteem of the phantom of power Pxx(w) in how much its expected value
does not coincide with the transformed one of Fourier of
autocorrelationship jxx(m), this result obtains itself is considering the
periodogramma like Transformed of Fourier of the esteem cxx(m) that of esteem therexx(m). The variance of the
periodogramma is 
and it does not stretch to 0
for N®¥ therefore the periodogramma is not a consisting esteem,
in particular have increasing oscillations to growing of N.
12) Periodogramma of a colorful noise:
where 
is periodogramma of a noise
the white man and Pxx(w) is the spectral density of power
of the colorful noise. The variance of the periodogramma is 
, therefore the periodogramma he is not a
consisting appraiser and it introduces of the remarkable oscillations
around the true value of the phantom.
13) Method of Bartlett for the esteem of the phantom:
Everyone consists in subdividing the sequence given x(n)
in K segments of M champions, is estimated the K periodogrammi in the
shape they is between independent they and
therefore the esteem of the phantom assumes the 
expression, its expected value is the convoluzione of the
true phantom Pxx(w) with transformed of Fourier of the
function the rectangular window correspondent to a periodogramma
calculated on N champions, the variance stretches to 0 to growing of
the number of N champions therefore the esteem of Bartlett is
consisting. It is had that to growing of the n° of
periodogrammi the variance the resolution of the phantom diminishes
but also.
14) Method of the windows for the esteem of the phantom:
The periodogramma is considered dulled 
having expected value 
e varianza 
from which it is
observed that the periodogramma asymptotically it is not polarized.
15) Method of Welch:
It is a modification of the method of Bartlett, in short
the window w(n) comes applied directly to every sottosequenza of
obtained data from the income sequence x(n), obtain therefore K
periodogrammi modified 
where 
is a necessaario factor of normalization so that the 
esteem asymptotically is not polarized.
16) Application of the FFT to the methods of Bartlett or Welch for the esteem of the phantom of potenza:
It is necessary to calculate for every sottosequenza 
by means of a FFT algorithm, they are estimated
then and they add one to the other until to i=K
finally the divided và result for KMU.
17) Application of the FFT to the calculation of esteem of the correlationship :
A first procedure is:
to) sequence of L is constructed one heads adding x(n) to (M-1) zeroes
b) the DFT is estimated on L aims 
con k = 0.1 … , L â " 1
c) is estimated the inverse DFT on L aims 
con m = 0.1 … , L â "
1
d) 
con m =
0.1 … , M â " 1
According to procedure it is instead:
to) the sequence 
is
constructed and if of it it calculates the transformed one on 2M
points