The impulsive answer
1) canonical Answers:
Impulsive answer w(t) : is the answer to the impulse of Dirac
Answer indiciale w-1(t): is the answer to the unitary step
2) indiciale Answer w-1(t):
It is the answer to the unitary step.
3) impulsive Answer w(t) :
It is the answer to the d of Dirac, is important because the transformed one of
Laplace of the impulse is 1 therefore 
therefore the impulsive answer corresponds to the antitransformed one
of the transfer function w(s).
4) Answer to regimen :
It is the part of the answer that remains when the transitory ones have been get exaustedded and are due to the forcing induced from the income
5) Answer in transitory :
6) associate Function of transfer of an elementary system of 1° the order and answers:
The impulsive answer is 
, is had that
the tangent in the origin to the impulsive answer intersects the axis
of the abscissas for t = t
value for which the amplitude has been reduced to 
of the maximum value. The indiciale answer is 
, is observed that a advanced time to 3 t
is necessary before that the
amplitude remains within 5% of the final value.
7) Time of arrangement:
It is the being necessary time because the amplitude of the escape remains within 5% of the final value.
8) Function of typical transfer of a system of 2° the order:
Where x are the breast of the included angle between positive the imaginary axis and the combining carrier the origin with one of the two complex poles conjugate to you while wn it is the module of such carrier.
9) Characteristic of the indiciali answers of a system of 2° the order in the variable case of x and wn constant:
It is had that for x = 0 the maximum sovraelongazione in how much is had the poles is imaginary while for x = 1 sovraelongazione in how much is not had the poles is real coinciding.
10) Characteristic of the indiciali answers of a system of 2° the order in the case of x variable constant andw n:
The maximum sovraelongazione remains invariata but to growing of wn it increases to the necessary time affinchè the escape catches up the regimen value.
11) Characteristic of the indiciali answers of a system of 2° the order in the case of w the variable constant and s:
The pulsation for which the maximum sovraelongazione happens is always the same one, s must naturally be negative otherwise has a limitless answer, the how much the more pole is close to the origin, much more elevated is the sovraelongazione.
12) Answer of a system any:
It is obtainable as combination of the answers of the elementary systems members of the 1° and 2° the order.
13) Answer of a system with 2 poles and one zero to varying of the position of the zero:
If the zero are next to the origin but in the semiplan negative it has a sovraelongazione of the answer while if the zero are in the positive semiplan it has a sottoelongazione, in any case the zero can only modify the amplitude of the answer, not the tipologia.
14) dominant Pole :
It is the main pole, normally more close to the origin, that is not true single if close to it there is a zero that of it renders residual the infinitesimal one and therefore a pole also more far away has greater infuence.
15) unstable System :
It introduces one exited limitless also in correspondence to incomes limits to you.
16) Ways :
Draft of terms whose sum gives place to the answer in the time of linear and stationary systems in presence of simple poles.
17) possible Definitions of stable system :
to) the answer it remains limited in
correspondence to every income limitato 
.
b) the transfer function possesses all poles allots to you in the left complex semiplan.
c) the impulsive answer is absolutely
sommabile that is is limited the integral 
From definition c) it follows that the integral is convergent > the impulsive answer stretches to 0 for t®¥.
18) Variation of the stability in function of the conditions begins them and of the income :
The stability is invariant for variation of the income or of the conditions it begins them, it is therefore an intrinsic property of the system.
19) asymptotically stable System :
It is a system that introduces an answer that converges asymptotically to zero for t®¥ .
20) Possible behaviors of a system with null conditions begin them subordinate to an income limited in duration :
to) limited answer, the system comes said stable.
b) divergent answer, the system comes said unstable.
c) limited answer that converges asymptotically to 0, the system comes asymptotically said stable.
21) necessary and sufficient Condition of stability :
The function of transfer of the system must only possess poles to negative real part or, this nully last only if with equal variety to one.
22) necessary and sufficient Condition of asymptotic stability:
The function of transfer of the system must have only poles to closely negative real part.
23) System to the stability limit :
A system is to the stability limit when there are poles to null real part with equal variety to one.
24) Stability BIBO:
Linear and stationary a system that has conditions begins them null is stable BIBO if to every it marks them of limited income u(t) corresponds one exited y(t) limited.
25) Tipologia of the poles for a stable system BIBO :
Draft of poles to closely negative real part.
26) Relation between a stable system BIBO and an asymptotically stable system :
A system is stable BIBO if and only if he is asymptotically stable, that is if the poles of the transfer function are all to closely negative real part.
27) necessary Condition so that the roots of a polynomial are all to negative real part :
The necessary condition is that all the coefficients of the polynomial are positi to you.
28) Realization of the table of Routh :
Given a polynomial in the shape 
one is come true table having numbered the lines to leave from the
degree of the polynomial until to zero. The first two lines
alternatively fill up posizionando the coefficients of the polynomial
on the 1ª and on the 2ª riga 
is
obtained therefore.
1° the coefficient of line 3 is obtained from the matrix 
and is worth 
while 2° the coefficient of line 3 is obtained from the matrix 
and vale 
, in both
the cases the division for b is necessary in the case is b<0 otherwise
can be avoided, but for all the line.
Analogous it is proceeded for the remaining coefficients, must be obtained that the coefficient of column 0 is equal to the famous term but this is not true in the case in which in order simplifying the calculations one is uniform entire line for a positive number.
29) Criterion of Routh :
The criterion of Routh concurs to realize a such table that the variations of sign of the first column are equal to the number of positive roots of the polynomial , therefore for the stability interests that not there is no variation of sign that is that the elements of 1ª the column are all positi to you.
30) Like replacing an equal coefficient to zero in 1ª the column of the table of Routh :
The two are possible following adulterate :
to) inverting the polynomial that is to
replace s with 
.
b) to multiply for (s a) in kind (s 1) or (s 2) they are created but of the problems in the case in which these values they are already roots of the polynomial .
31) Like replacing one line with coefficients all null ones in the table of Routh :
The coefficients of the previous line in order to write a polynomial of equal degree to the order of the same one are used (…are always a n° equal), the polynomial therefore found it must it are derived and its coefficients become the coefficients of the null line.
32) direct Measure of the impulsive answer and its validity :
It completes itself sending in income to system 3 rampe with opportune slopes so as to to create a shape of trapezial wave that approximates the ideal impulse, the escape of the system approximates the impulsive answer well on condition that the duration of the income push-button is much minor of the smallest constant than time of the system, but the time constants are ignote therefore in order to determine the duration of the impulse do not make other that to alter the rampe so as to to halve the period of the impulse, and to the contempo if of it it increases the amplitude so that the area remains unitary, iterando the procedure is reached the moment in which the answer it remains invariata, well the period of the corresponding impulse turns out to be much minor of the smallest constant than time of the system.
The problem is that in order to maintain the impulse of unitary area for small constants of time must be demanded amplitudes of marks them many elevating, that it can create of the saturation problems.
33) Measure of the indiciale answer :
The step comes simulated by means of the difference of two rampe of slope 1/T, the answer of the system comes said pseudoindiciale, is not applicable in the case the system present already a pole in the origin in how much will have in escape a rampa that it does not concur to obtain turns out to you.
34) ergodico Process :
Draft of a stationary process which it can only generate functions with null or unitary probability.
35) Function of autocorrelationship :
It is a function jf that currency the degree of correlation of a function f(t) with if same, is had:
or also
this last one is written in terms of a delay and therefore from a physical point of view it is more meaningful.
36) Function of mutual correlation :
It is a function jfg that currency the degree of correlation between two functions f and g, is had:
in the truth having to operate with ended times of integration it is necessary to carry out an esteem that the integral consists simply in taking therefore com' is without to make of the limit.
37) Relation of Wiener - Lee :
When it is wanted to be carried out an indirect measure of
the impulsive answer can be inserted a correlatore that exactly
calculates the function of mutual correlation between marks them of
income and it marks them of escape of the system in fact replacing
the integral of convoluzione in the function of mutual correlation
obtains 
that being famous it marks them of
income u(t) and therefore its function of autocorrelationship , through a
deconvoluzione gives back the impulsive answer.
38) Property of the noise white man :
The noise white man is characterized from the 4 following property :
to) medium null
b) density of probability of Gaussian or uniform type
c) stazionarietà and ergodicità
d) function of equal autocorrelationship jr (t) to an area impulse proporziona them to variance sr2.
39) indirect Measure of the impulsive answer with and without the normal income :
to) with disinserito income
Sending in income to the system a noise white man it is had that the function of mutual correlation between income and escape of the system found from the correlatore is equal to the product of variance sr2 of the multiplied noise binaco for the impulsive answer and is therefore proporziona them to it.
b) with inserted income
The sum is sended in income to the system of marks them u(t) and of the noise white man r(t). To the correlatore it is sended instead marks them of escape y(t) and the noise white man, obtains therefore that the function of mutual correlation noise-escape still gives back the impulsive answer multiplied for the variance of the noise more a term that can be rendered null on condition that the correlation between marks them of income and the noise is null.