Elements of elaboration of mark them

Invariant linear transformations time

1) Function of having transfer of the quadripolo complementary to quadripolo the function of H(f) transfer:

in fact the quadripolo it possesses a delay sure that place to the denominator becomes an advance payment and goes therefore neutralized through the complex exponential negative. It marks them that she crosses a quadripolo and its complementary one reaches therefore in only attenuated escape.

 

2) linear Elaboration of champions:

It marks them s(t) can be represented in the sampled shape , where is one function of base to unitary energy. Applying in income to quadripolo a LTI the sampled sequence x(n) the answer in terms of champions is still obtained where h(n) discreet equivalent is the impulsive answer. So that there is reversibility is necessary that the two quadripoli have the same band but the phantom can have various course, remembering in fact that the phantom of a process championship in band base is the phantom of escape P_Y(f) has the same expression but covarianza c_xx is in various kind.

Transformations in mark squared them

3) It marks squared them:

The numerical flows are in kind veicolati from mark them real in squared shape where x_qk pu² to only assume pertaining values to with discreet, succeeding to carry in this shape also marks them analogic is in a position to carrying out an only trattazione of the possible elaborations. The theorem of Nyquist guarantees us the possibility to replace marks them with of its champions captures to you with a double frequency regarding the maximum present frequency in marks them therefore is permissible in theoretical way the formation of marks them in squared shape obtained from x(t) by means of a maker of marks squared them substantially constituted from a switch whom it samples to moment t₀ , an integrator that maintains and in escape from it a switch towards mass that closes to t T₀ . Unfortunately quadripolo complementary that would have to guarantee the reversibility has function of transfer that introduces a discontinuity in the gain that demands an infinite selettività and therefore is extremely difficult to realize. In the case of a numerical flow the quadripolo complementary he is extremely simple and only it consists in an ulterior maker of marks squared them having the same temporizzazione, however in presence of it disturbs has an only formal regeneration that must be continuation from one decision procedure.

 

4) spectral Characteristics of the process with realization in squared shape :

Beginning from a X(t) process limited in band is obtained marks them in squared shape having spectral density che is in relation with the spectral density of the process entering by means of .

Principles of codify

5) Codifica with redundancy :

It is one codifies that it is applied with the aim to improve the performances of an imperfect system of transmission, in particular comes independently from the characteristics of the modulation employed in the transmission system, come inserted of the bit in excess to the aim to concur the detection of the error that can carry to the correction of the same (FEC) or to the demand for rebroadcast, in any case an improvement of DRINKING is had that is the expected value of the relationship between the wrong number of the bit pertaining to a sequence the much long and n° of the bit that they compose the same sequence.

The added one of bit in excess provokes an increase of the binary rhythm in escape R_x regarding that one in R income_u and comes expressed by means of the frequency of codifies where n it is the number of figures that compose the word in income to the coder while k it is the number of figures of the word corresponding emitted from the coder.

The techniques of codify with redundancy main are codify it to delineate to blocks and it codifies it convoluzionale.

 

6) linear Codifica to blocks:

Beginning from a binary sequence u(n) the coder forms a block constituted from k bit in a registry of ugual largeness, by means of linear combinations of this bit comes formed one word of code x in a registry with n > k bit.

It is had therefore that 2ⁿ-2^k configurations that do not belong to the code come only produced from an error and therefore possibly come found and corrected from the decoder.

 

7) systematic Codifica:

It is one of the possible linear codifiche to blocks, in short the first k bit of the word formed from the coder are equal to k the bit of the income word u while remaining n-k the bit comes obtained from the previous ones by means of linear combinations in arithmetical module 2.

An example of codifies systematic is codifies it (2.1) of Manche ster it associates to word u = 0 in income the word

y = 01 in escape and to the word u = 1 word y = 10 while the words y = 11 ed y = 00 are only introduced to the decoder in error case that however cannot be corrected in how much cannot be understood which of the two bit of the brace is that wrong one. An other example of codifies systematic is codifies it (7,4) of Hamming in which the remaining 3 bit of the word produced from the coder are bit 5 u₁... u₂ ... u₃ , the bit 6 u₂...u₃...u₄ and ₄ bit 7u₁ ...u₂ ...u in such a way thanks to the remarkable redundancy is had that the code words differ between of they at least in 3 positions therefore are possible to reveal the presence one or two errors and to correct of one.

 

8) convoluzionale Codifica:

Draft of one is codified with memory is had in fact that the income sequence u(n) goes to fill up a registry to L bit, from this by means of linear combinations in arithmetical module 2 they form n bit that then come serializzati going to in short form the sequence codified x(n) for every binary figure of income if they produce some n-1 redundant that it determines that the binary rhythm in escape is n times greater of the binary rhythm in income, such factor can be reduced paralleling the word u(n) and going to fill up k registries to L bit, the relation between the binary rhythms becomes .

 

9) Codifica differentiates them:

It is one codifies lacking in redundancy that is used in the case of codifies with memory where an error propaga determining a decoded binary sequence that from the error in then it is the denied one of that correcting. The method in which such disadvantage it comes eliminated consists in associating the information not to the levels but to the variation of the same ones, that as an example obtains making that if in the income sequence is 0 then in that one of escape it maintains the bit that there was previously while if in the income sequence is then in the escape sequence inserts the denied one of the bit that there was previously. During decodification other is not made that to compare every figure with the previous one.

 

10) Codifica with change of the cardinalità:

The income sequence y(n) goes to fill up a registry to b bit where b the to every word is function of cardinalità M of the M-nario entirety second y comes associated a pertaining symbolz _q to with discreet.

A typical example is codifies it of Gray in which to binary words of the income sequence that only differ for a bit they come associates adjacent elements to you of with of the symbols.

Modulation to product

11) It marks modulated them to product:

Multiplying it marks them in band carrying base b(t) with a harmonic is obtained marks them whose phantom is constituted therefore from two retorts of the phantom P_b(f) of the process in traslate of f _c ±andreduced band base of ¼.

The reversibility obtains thanks to a demodulatore in which it marks them s_x(t) comes multiplied for a produced harmonic oscillation 2c(t) from a synchronized oscillator obtaining from which pu² to riottenere the process in band base by means of a filter it low-pass filter with frequency of cut f_c .

 

12) real Oscillator:

The real oscillator comes obtained by means of a made amplifier to work in conditions of instability by means of a selective circuit that determines the value of the pulsation, the oscillation that derives some is:

where to_N(t) amplitude noise is the realization of a called process while j_n(t) is the realization of a called process phase noise both are in absolute value much minor of 1 while x(t) is the realization of a called process instability of the oscillator and has had to variations in the time of the elements that condition the frequency of the oscillation.

13) Oscillating coherent and not coherent:

The oscillation produced from a coherent oscillator introduces a almost constant instability in the time, its expression is therefore and turns out constituted from a fundamental frequency moved respect to f_{a 0} and spectral density of noise that can be filtered via by means of a filter pass-band centered on f₀ . The stability can be estimated by means of the relationship that are worth 10 ^-3typically reaching oscillating10 ^-5 for quarzati and to quarzati10 ^-6 for oscillating termostata to you.

A not coherent oscillator produces instead a oscillation characterized from a variable instability in the time in not negligible way, is the case of the oscillation produced from a LED or a LASER.

 

14) Describe the ring to phase coupling:

A free oscillator is had of which the frequency can be varied acting directly on a largeness to the heads of a member, it can be synchronized with a coherent oscillation in fact carrying out the product between the two oscillations, and leaking it is obtained marks them proporziona them to the phase error and by means of quadripolo a Q_L can be varied so as to to couple the two oscillating ones.