Z (2.48) is taken

(2.49)

In order to fix the fact that the Walsh functions are equal to ±1, we can write (2.49) for the visual

(2.50)

de a p (k) = 0 or 1 signifies the sign of the Walsh function on the interval
Apply the Walsh spectra.

1. The Walsh spectrum of a rectangular pulse s(t) = 1, 0 ≤ t ≤ t (Fig. 2.9)

Z (2.50) is known

The Walsh spectrum of a direct-current impulse to lie in the form of a relationship between t and T. When τ/T = 2 v de v is a positive number, the value of the Walsh functions is taken away from the improvement

The distribution of the rectilinear impulse behind the Walsh functions can be seen

The spectrum is composed of 2 V warehouses with the same amplitudes, which equal 1/2 V. Spectrum revenge kіlkіst kіlkіst warehousing. At t/T≠ 2 V the structure of the spectrum changes.

Fig. 2. Spectrum of a volcanic pulse (Fig. 2.10)

manually go to the unlimited hour x = t/T

Valid until (2.50) we know:

The Walsh spectra with Harmuth and Pele numbering are shown in Fig. 2.10, b and c.

3. Walsh spectrum of a sinusoidal pulse (Fig. 2.11)

For sinusoidal pulse

passing to a timeless hour x = t/T, we write

Z (2.50) for the Harmuth system is known (Fig. 2.11):

The Walsh spectra of the signal, which can be seen with the numbering of Harmuth and Pele pointing in Fig. 2.11,6 and c.

2.7A. The power of the Volsh spectra

When analyzing signals with additional Walsh functions, it is important to check the power of the distribution of signals in the Walsh basis - Walsh spectra.

1. The spectrum of the sum of the signals to the sum of the spectra of the skin signal.

The signal spectrum of the system of Walsh functions is determined by the expansion coefficients (2.47). For sum signals

(2.52)

de a pc is the distribution coefficient for the signal s k (t).

2. Increasing the signal to the Walsh function with the number n changes the numbers of the coefficients of the distribution of k zgіdno from the law of the two-dimensional zsuvu for module two

3. Walsh spectrum for additional signals s 1 (t) and s 2 (t). assigned at intervals. Such functions describe periodic signals with a moderate tension.

For the pair function s(t), which means that z (3.2),

(3.3)

for an unpaired function s(t):

(3.4)

Sound the hour for the analysis of the signals

(3.5)

A periodic signal is represented as a sum of harmonic warehouses with amplitudes A n i cob phases.

The sequence of amplitudes (D,) determines the amplitude spectrum, and the sequence of cob phases (n) - the phase spectrum of the signal (Fig. 3.1, a). As we see from (3.5), the spectra of periodic signals are discrete or linear, the frequency sampling interval is higher than the frequency of the signal 1 = 2π/T.

The trigonometric Four's series can be written in complex form

(3.7)

(3.8)

The transition from (3.1) to (3.7) is obvious from the improvement of the Euler formula

(3.9)

Coefficient of s n for a wild fallout є complex values

With a different complex form in the Fourth series, the signal is assigned to a series of complex amplitudes (z n). Modules of complex amplitudes | h n | describe the amplitude spectrum, the argument n is the phase spectrum of the signal (Fig. 3.1.6).

Presenting (3.8) to the viewer

(3.11)

As you can see from the records of the virus, the amplitude spectrum has a pair, and the phase spectrum has an unpaired symmetry.

(3.13)

3.2 and (3.11) stand out

Like a butt, we can look at the periodic sequence of rectilinear impulses (Fig. 3.2 a). When expanding the periodic sequence of rectilinear pulses, the trigonometric Four's series (3.2) takes away the amplitude and phase spectra of the viewer (Fig. 3.2, b):

When vikoristanny complex form series Four'є
from (3.8) we see:

Amplitude and phase spectrum of the signal equal

The boundary view is low Fur'є є іntegral Fur'є. The periodic signal at T → ∞ becomes non-periodic. Substituting (3.8) for (3.7), we write

(3.16)

Harmonic signal analysis

Reversing (3.16), at T→∞ (for which direction ω 1 → dω і Пω 1 = ω), we can

(3.17)

Fourth integral is written at the square arms, vin describes the spectral width of the signal

Viraz (3.17) on the lookout

Recordings of spіvvіdnoshennia represent the direct transformation of Fur'є. The stench gets stuck in the harmonic analysis of non-periodic signals.

3.2. Harmonic analysis of non-periodic signals

The direct reversal of Four's transformation establishes a mutually unambiguous difference between the signal (tim-hour function that describes the signal s(t)) and the same spectral width S(ω):

(3.18)

Validity for Four'e is significant:

(3.19)

Intellectual basis for the transformation of Fur'є є absolute integration of the function s(t)

(3.20)

In practical additions, sruchnіshim є umova іtegrovannostі square ієї functions

(3.21)

For real signals, mind (3.21) is equivalent to mind (3.20), but there is an obvious physical difference: mind (3.21) means to reduce the energy of the signal. In this rank, we can vvazhat we can zastosuvannya transforming Fur'є to signals with obmezhenoyu energy. Tse non-periodic (impulse) signals. For periodic signals, laying out on harmonica

no warehouses turn for help in the Fur'e row.

Function S(ω)

de Re, lm - descriptive part of the complex value; |s(w)|, φ(oo) - modulus and argument of a complex value:

The module of the spectral thickening of the signal | S(ω) | describes the distribution of amplitudes of harmonic warehouses by frequency, is called the amplitude spectrum. The argument φ(ω) gives the phase to the frequency, which is called the phase spectrum of the signal. The amplitude spectrum is a pair function, and the phase spectrum is an unpaired function of frequency

With the improvement of the Euler formula (3.9) for S(ω), we can write down as

(3.24)

Since s(t) is a pair function, then (3.24) is taken

(3.25)

The function S(ω), as seen from (3.25), is a real function. The phase spectrum is displayed as

(3.26)

For an unpaired function s(t) from (3.24) we take

(3.27)

The function S(ω) is purely explicit, the phase spectrum

(3.28)

Whether a signal can be given as the sum of paired s h (t) and unpaired s H (t) warehouse

(3.29)

The possibility of such a manifestation becomes sensible to the improvement of advancing equivalences:

З (3.24) and (3.29) are taken

(3.30)

Also, for the dynamic and visible parts of the spectral width of the signal, you can write:

In this rank, a distinct part of the spectral thickening represents the transformation of Fur'є into a paired warehouse signal, and a visible part - into an unpaired warehouse signal. The descriptive part of the complex spectral thickening of the signal is a paired one, and the obvious part is an unpaired function of the frequency.

Spectral thickening of the signal at ω = 0

(3.31)

more areas under the curve s(t).

How to apply the spectrum of such signals.

1. Rectangular pulse (Fig. 3.3 a)

de i - trivality of the impulse.

Spectral width of the signal

Graphs of the amplitude and phase spectra of the signal are shown in fig. 3.3, b, art.

2. Signal, which is described by the function

The spectral width of the signal is determined by the frequency

Integrating by parts n-1 times, at least

Signal (Fig. 3.4 a)

maximum spectral width

Graphs of the amplitude and phase spectra of the image in fig. 3.4, b, art.

Signal (Fig. 3.5 a)

maximum spectral width

Graphs of the amplitude and phase spectra - fig. 3.5, b, art.

The number of applications is bigger than the table. 3.1.

The alignment (3.18) and (3.8) show that spectral width single impulse at τ<

With the improvement of the assigned spіvvіdshlennâ vyznachennya spectrum of the periodic signal hour can be forgiven, vikoristuyuchi transformation Fur'є (3.18). The coefficients in the Fur'є series are known as

(3.32)

de S(ω) - spectral thickness of one pulse.

In this way, with the specified amplitude and phase spectra of periodic signals in the mother’s chest on the edge of the onset:

The coefficient 1/T can be considered as a frequency interval between the suicidal warehouse spectrum, and the spectral width as a ratio of the amplitude of the warehouse signal to the frequency interval, which means the amplitude. Looking back at it, let's understand the term "spectral wideness" more clearly. Bezperervnі amplitude and phase spectra of a single pulse є outgoing discrete amplitude and phase spectra of a periodic sequence of such pulses.

For additional help (3.33), the results of guidance in Table. 3.1 can be used to select the spectra of periodic sequences of pulses. Such a pidkhid is illustrated by such butts.

1. Periodic sequence of rectilinear pulses (Table 3.1 p. 1), fig. 3.2.

Recordings viraz repeat the result of the butt of clause 3.1.

2. Periodic sequence of meander impulses (Table 3.1 p.2), fig. 3.6 fig. 3.2.

3. Periodic sequence of exponential impulses (Table 3.1, item 8), fig. 3.7.

Table 3.1

Spectrum signals

3.3. Frequency spectra of signals represented by the narrowed Four's series

When a signal is given, it's like a zagalnenny Four's series, the transformation of the Four's basic functions is corisal. Tse allow the spectrum of the basis of different orthogonal systems to pass to the frequency spectrum. Below are examples of frequency spectra of various types of signals, which are described by the basic functions of orthogonal systems.

1. Signal Legendre.

The transformation of Fur'є the rich member of Legendre (section 2) may look

(3.34)

n \u003d 1.2, ... - Legendre rich term; - Bessel function.

Vikoristovuyuchi (3.34), according to the signal given to the watchful row

with coefficients

(3.35)

Viraz (3.35) describes the spectral thickness of the signal s(f) in the visual series.

Graphs of the warehouse spectrum with numbers 1 - 3 are shown in Fig. 3.8.

2. Signal Laguerre.

The transformation of Fur'є functions of Laguerre may look

(3.36)

n = 1,2, ... - Laguerre functions.

Vykoristovuyuchi (3.36), according to the signal presented in the visual row of the Laguerre multiplier (section 2)

with coefficients

you can go to the spectral thickening of the signal

(3.37)

3. Signals to Yermita.

The transformation of Fur'є functions of Yermita may look

(3.38)

n = 1,2, ... are Hermit's functions.

Z (3.38) follows that the functions of Hermit may be the power of transformation, that is. the functions of this transformation Fur'є equal (to exactness up to the constant coefficients). Vykoristovuyuchi (3.38), according to the signal presented in the visual row of layout along the Hermit's leg

with coefficients

you can go to the spectral thickening of the signal

(3.39)

4. Signal Walsh.

The frequency spectra of the Volsh signals (signals that are described by the Volsh functions) are assigned to the upcoming transformations of Four'e:

(3.40)

de wal (n, x) - Walsh function.

So, as the Walsh functions can think of N number of constant values,

de x to - the value of x on the to-mu interval.

Z (3.41) is taken

de

Since the Walsh functions take on the value ±1, then (3.42) can be written as

(3.43)

de n (k) = 0 or 1 is the sign of the function wal (n, x k).

On fig. 3.9 shows the graphs of the amplitude spectra of the first six Walsh signals.

3.4. Spectra of signals that are described by non-integrating functions

The transformation of Fur'є іsnuє is only a signal of final energy (for those who win the mind (3.21)). Expand the class of signals, analysis of Four's transformations, allowing a sutto formal reception, foundations on the introduction of the understanding of the spectral width of the impulse function. Let's take a look at such signals.

1. Impulse function.

Impulse function (or - function) is displayed as

(3.44)

Significant impulse function

(3.45)

The spectral width of the impulse function is significant as

(3.46)

Amplitude spectrum of older units, phase spectrum φ(ω) = ωt 0 (Fig. 3.10).

Zvorotne transformation Fur'є daє

By analogy with (3.47) for the frequency domain, we write

(3.48)

Vykoristovuyuchi otrimani virazi, significantly spectral denseness of some kinds of signals, which are described by functions, for which there is no transformation of Fur'є.

2. Constant signal s(t) = s0.

Z urahuvannyam (3.48) is taken away (Fig. 3.11)

(3.49)

3. Harmonic signal.

Spectral thickening of the signal of the view with improvements (3.48) at the view

At ? = 0 (Fig. 3.12)

For signal

(3.53)

by analogy with (3.52) we know

4. Single step function.

(3.55)

A single step function σ(t) can be considered as a boundary view of an exponential momentum

The exponential momentum can be represented by a sum of paired and unpaired warehouses (3.29)

orthogonal functions. As the layout sounds, the Four's transformation, the layout for the Walsh functions, the wavelet transformation and that in.

Basis functions

Mathematical tribute

The spectrum of the signal can be recorded through the transformation Four'є (it is possible without a coefficient 1 / 2 π (\displaystyle 1/(\sqrt (2\pi )))) at a glance:

S (ω) = ∫ − ∞ + ∞ s (t) e − i ω tdt (\displaystyle S(\omega)=\int \limits _(-\infty )^(+\infty )s(t)e^ (-i\omega t)dt), de ω (\displaystyle \omega)- Cutoff frequency equal 2 π f (\displaystyle 2\pi f).

The spectrum of the signal is a complex value and is given to the viewer: S (ω) = A (ω) e − i ϕ (ω) (\displaystyle S(\omega)=A(\omega)e^(-i\phi (\omega))), de A (ω) (\displaystyle A(\omega))- amplitude spectrum of the signal, ϕ (ω) (\displaystyle \phi (\omega))- Phase spectrum of the signal.

Like a signal s(t) (\displaystyle s(t)) understand

Bring the coefficients to the Kotelnikov series s(t), the value of the signal at the moment and hour t=nt bud.

Bring that the functions are valid sinc( t-nt e) and sinc( t-mT e) orthogonal at n¹ m.

Define the spectral width of the impulse given by the analytical virus s(t)=sinc( t-nt e).

Why is it impossible to use the basis of the function, which describes the signal, the frequency spectrum of the frequency spectrum?

9. Signaling by Walsh functions

In 1923 p. American mathematician Walsh J.L. Discrete signals with the improvement of the Walsh functions (FU) are a complete system of orthogonal functions of the type of a rectilinear wave. The area of ​​the Walsh function blockage, to reach a large number, is constantly expanding.

Walsh functions can be graphically displayed in different ways. However, on the interval of its appointment, the stench accumulates only two values: +1 and -1. For the FU students, call to introduce a bezrozmirne hour, otzhe.

On fig. 9.1 representation of the first 8 Walsh functions on the interval of the value of the argument.

Mal. 9.1. Walsh functions, ordered and numbered according to the number of sign changes on the interval.

Please accept wal k(q) spelled names Walsh. Index k indicate the number of sign changes (the number of changes of zero level) by the function on the interval of appointment. That's half the value k otherwise called a part of wal k(q). The area of ​​іsnuvannya FU is characterized by the expansion of the basis, de n=1,2,3,.… 9.1 expansion to the basis.

Walsh functions of orthonormalization on the interval:

The Walsh functions may have the power of multiplicativity, that is. multiplying two FU gives another FU, moreover

de operation designates the summation by module 2 according to the rules:

1Å1=0; 0Å0=0; 1Å0=1; 0Å1=1.

Multiplying FU itself vin gives a function of zero order, the shards of the result come out less to see. in such a manner,

Reproduction be-like FU on a function of the zero order, tobto.

do not change the first function. For whom, the entire sensory FU plays the role of a “single” function.

Naturally, the entire orthonormal system of Walsh functions allows one to represent whether signals are Walsh-Four's series.

.

The procedure for determining the amplitude of the cutaneous direct harmonic in the Walsh-Four series is even simpler: with an input signal s(t) for k-those "harmonics" coefficient is determined by the formula

.

Butt: lay out the Walsh-Four function in a row at intervals, having grown rich with eight members of the distribution (basis).

Passing to the unfathomable hour, next to know. Oskіlki function is set s(t) is unpaired, and all Walsh functions with paired indices, including zero, are paired in fig. 9.1, then create , which will be unpaired functions i, then, the integral of these creations is equal to zero: s 0 = 2 = 4 = 6 = 0.

Now we calculate the coefficient:

Cost factor:

,

de assigned, and .

You can remove clumsy tabs

In this order, the laying out of the sinusoidal coli s(t) at the basis of the Walsh functions N\u003d 8 may two non-zero spectral warehouses with amplitudes

.

The result of signal approximation let's shorten a number of the Walsh functions and the spectrum of the signal in the basis of the Volsh functions of the representations in Fig. 9.2, aі b obviously.

Mal. 9.2. Sending a signal to spreading on an orthogonal basis of the Walsh functions

Root-mean-square pardon given to the signal is truncated next to the Walsh functions to become

Understanding, the arrangement of sinusoids in the Four's series for trigonometric functions gives better accuracy. Stovidsotkova accuracy is ensured by the order that only one member can be avenged . Ale arranging a rectangular meander function, such as wal 1 (q), in a series of Fur'є

with the loss of all two members in a row, I’ll be safe richer accuracy for a mid-square pardon, and myself, as if yelling s. Naturally, the spectrum of a direct-path function behind the Walsh functions can only be replaced by one warehouse function that can be represented exactly by it.

This example illustrates the fact that for a specific type of skin signal, it is such a basic system that gives the most compact detection of the signal with a given accuracy (or the most accurate detection when setting the number of members of the distribution).

The Walsh functions are easily generated by digital signal processing systems, which are based on a modern element base.

CDMA tie-down system

In the rest of the years, significant progress in telecommunication technologies has reached the beginning of the transition to digital video communication, which, in its own way, is based on the rapid development of microprocessors. One of the best applications of this is the emergence of this technology in the implementation of communication technology with digital noise-like signals based on the method of rich-station access with coded subdivision of channels (CDMA - Code Division Multiple Access), at the nearest future of the new capital to obscure all NMT, other, and analogues AMPS is one of the strong competition for digital technologies such as GSM.

The miraculous power of digital communication from noise-like signals - the protection of the communication channel from overreaching, overshooting and listening. To the very same time, this technology was later developed and victorious for the US military forces, and only recently the American company Qualcom created the IS-95 (CDMA one) standard on the basis of this technology and transferred it to the commercial victoria. There are six companies that already issue the standard for this standard: Hughes Network Systems, Motorola and Samsung.

Significant characteristic and principle of functioning

The principle of the work of the systems of the stiltnikovy connection with the coded bottom of the channels can be explained on the stepping butt.

Suppose you are sitting at a restaurant. There are two individuals at the leather table. One pair speaks English among themselves, another Russian, a third German, etc. To go out so that in restaurants everything is moving at the same hour on the same frequency range (movie from 3 kHz to 20 kHz), when you speak with your opponent, you understand only a little yoga, but you can feel everything.

So, in the CDMA standard, the information that is transmitted on the air, from the base station to the mobile one, or navpaklya to all subscribers in the network, and even if the subscriber understands only that information, as it is recognized for the new, tobto. Russian intelligence is less than Russian, German is less than German, and the solution of information is visible. Mova splkuvannya at the same time є code. In CDMA, it is organized for the data blocking of data encoding that is transmitted, which is more precise, then for this reason the Walsh function multiplier block is used.

On the basis of the GSM standard, which is a kind of TDMA (Time Division Multiple Access - a rich station access with a time-based channel, so that a few subscribers can talk on the same frequency, like in CDMA, but on the other side of CDMA, at a different hour), IS-95 standard

CDMA is called a wide-range system and the signals that go on the air are noise-like. Shirokosmugov - to the one who occupies a wide range of frequencies. Noise-like signals - to those who, if on the air at the same frequency, at the same hour, have a few subscribers, the signals are superimposed one on one (you can detect noise at the restaurant, if everyone is talking at the same time). Pereskodostіyka - to that, when viniknennі in a wide range of frequencies (1.23 MHz) signal-pereskodі, vіdіznamu (<150кГц), сигнал примется почти неискаженный. За счет помехоустойчивого кодирования потерянные данные система восстановит, см. рис 1, где показан полезный сигнал и помеха (СЗС - селективная помеха).

And the GSM standard does not have the same. Through those who are GSM on the cob, he himself is very cosmopolitan. The width of the smuga, which is victorious, is 200 kHz.

Qualcom's CDMA system is warranted for use in the 800 MHz frequency band. The CDMA system was inspired by the direct frequency spectrum spreading method based on a selection of 64 types of sequences formed from the Walsh function law. For the transmission of voice messages, a speech-transforming attachment was chosen by the CELP algorithm with a speed of 8000 b/s (9600 b/s channel). Possible modes of operation on speeds 4800, 2400, 1200 bit/s.

Do the CDMA system channels freeze with coded code? (in channels from the base station) and 1/3 (in channels from the dead station), Viterbi decoder with soft solutions, interleaved notifications that are transmitted. Zagalna smuga channel zvyazku become 1.25 MHz.

The main characteristics are indicated in the table.

Transmission frequency range MS	824.040 - 848, 860 MHz
BTS transmission frequency range	869.040 - 893.970 MHz
Visible instability of carrier frequency BTS	+/- 5*10^-8
Visible instability of carrier frequency MS	+/- 2,5*10^-6
Type of carrier frequency modulation	QPSK(BTS), O-QPSK(MS)
Width of the spectrum of the modified signal: beyond minus 3 dB for equal minus 40 dB
PSP clock frequency M-functions	1.2288 MHz
Number of BTS channels per 1 carrier frequency	1 pilot channel 1 sync channel 7 channels of personal viklik 55 channels
Number of channels MS	1 access channel 1 channel call
Data transmission speed: At the sync channel The channel has a personal call and access The channels have a call	9600, 4800 bps 9600, 4800, 2400, 1200 bps
Encoding on BTS channels	Short code R=1/2, K=9
Encoding on MS transmission channels	Short code R=1/3, K=9
Necessary for the reception of the energy bit of information	6-7 dB
The most effective way to relieve BTS tension	50 W
The most effective viprominuvanation of MS tension	6.3 - 1.0 W

Standard victories have a different processing of incoming signals, which come with different noises, and further away from you, which significantly reduces the negative impact of the effect of richness of change. In case of different processing of changes at the skin canal, 4 correlators work in parallel, and 3 corelators at the rough station. The presence of parallel working correlators allows you to set up a soft mode of "relay transmission" at the hour of the transition from the stylist to the cell.

The soft mode of "relay transmission" is used for the account of a roaming station by two or more by base stations. The transcoder, which is to enter the warehouse of the main possession, evaluates the quality of the received signals in two base stations frame by frame. The process of selecting a short frame should be brought up to the point where the resulting signal can be formed in the process of uninterrupted switching and distant "gluing" of frames, which are received by different base stations, which take part in the "relay transmission".

Communication protocols in CDMA, like in AMPS standards, are based on different logical channels.

In CDMA, the transmission channels from the base station are called forward (Forward), those received by the base station are called reverse (Reverse). The structure of CDMA channels in the IS-95 standard is shown in Fig:

Direct channels in CDMA:

1. Pilot channel - vikoristovuetsya ruhomy station for cob synchronization with a measure and control over the signals of the base station by the hour, frequency and phase.
2. Synchronization channel - ensures the identification of the base station, the rate of change of the pilot signal, as well as the phase of the pseudo-reciprocal sequence of the base station. After the completion of the appointment of the stages of synchronization, the process of setting up the plant is started.
3. Vikliku channel - vikoristovuetsya for vikliku ruhomoy station. After receiving a call to the ruhoma signal, the station transmits an acknowledgment signal to the base station, after which the call to the remote station transmits information about the establishment of the call and recognition of the link to the channel. The personal call channel starts working after the station takes all the system information (carrier frequency, clock frequency, signal jamming by the synchronization channel).
4. Direct access channel - assignments for the transfer of current alerts and data, as well as control information from the base station to the hand.

Return channels in CDMA:

1. Access channel - secure communication between the primary station and the base station, if the primary station still has a victorious channel for traffic. The access channel is selected for the installation of calls and confirmations for notifications that are being forced on the call channel, the command is to ask for registration in the border. Access channels are connected by dial-up channels.
2. Return traffic channel - ensures the transmission of current notifications and information from the old station to the base station.

The structure of the transmission channels of the base station is shown in Fig:

The skin logical channel is assigned its own Walsh code. For one physical channel, there can be 64 logical channels, because Walsh's sequences, which are logical channels, in total 64, each may be 64 bits. Three of the 64 channels on the 1st channel are assigned the first Walsh code (W0) to which "Pilot channel" is assigned, thirty other Volsh codes (W32) are assigned to the next channel, the next 7 channels are assigned their own Volsh code (W1, W2, W3 ,W4,W5,W6,W7) which channels are used to call, and 55 channels, which are no longer available, are recognized for data transmission over the "Direct Traffic Channel".

When you change the sign of the bit of the informational announcement, the phase of the Walsh sequence, which wins, changes by 180 degrees. Since these sequences are mutually orthogonal, then mutually switch between transmission channels of the same base station every day. Crossovers over the transmission channels of the base station create only land base stations, which work in the same radio frequency mix and vicorize the very same bandwidth, but with other cyclic disruptions.

The order of passing the current data on the mobile station until the moment it is sent to the air.

Let's look at the block diagram of the traffic return channel. At the direct and ductal channels, the scheme is repeated; Depending on which channel is victorious at a given moment, such blocks of the scheme are turned off.

1. Movny signal nahodit on movny codec.
   At which stage the current signal is digitized and squeezed behind the CELP algorithm.
2. They gave a signal to go to the block of a stable code until the code was changed, which can correct up to 3 pardons in a data packet.
3. They gave the signal to go to the signal interleaving block.
   A block of appointments to fight against bundles of pardons on the air. Bundles of pardons - creating a lot of bits of information later.
   The principle is this. The flow of data is recorded in the matrix in rows. As soon as the matrix is ​​filled, we start from it to transfer information to the columns. Henceforth, if the ethers are created after a sprinkling of bits of information, I will receive a pack of pardons, passing through the return matrix, transforming into single pardons.
4. They gave a signal to come at the coding unit (for listening).
   A mask (sequence) of 42 beats is imposed on the information. Tsya mask is secret. In case of unauthorized transfer of data to the air, it is impossible to decode the signal without knowing the mask. The way to enumerate different values ​​is not efficient, because when generating mask numbers, sorting through different values, it will be possible to generate 8.7 trillion masks with a total of 42 bits. A hacker, using a personal computer, passing a signal through a skin mask and converting it to a sound file format, then, recognizing it for a movie, spend a lot of time.
5. Block interleaved Walsh code.
   The digital data flow is multiplied by the sequence of bits generated by the Walsh function.
   At this stage of coding, the signal needs to be expanded to a frequency range, tobto. The skin bit of information is encoded by the sequence induced by the Walsh function, up to 64 bits. That. the speed of data flow at the channel is increased by 64 times. Also, in blocking the modulation of the signal, the ability to manipulate the signal increases, the expansion of the frequency spectrum.
   Also, the Walsh function is valid for providing non-essential information from other subscribers. At the beginning of the call session, the subscriber is assigned a frequency, on the basis of which there is one (out of 64 possible) logical channel, which is assigned the Walsh function. At the moment when the signal is received, the circuit will pass at the gate. The received signal is multiplied by the Volsh code sequence
   After the result of the multiplication, the correlation integral is calculated.
   If the Z threshold is satisfied with the boundary value, then the signal is ours. The consistency of the Walsh function is orthogonal and may have good correlation and autocorrelation power, so the ability to confuse your signal with someone else's is 0.01%.
6. The signal multiplication block on two M-functions (M1 - up to 15 bits, M2 - up to 42 bits) or else they are called PSP-pseudo-advanced sequences.
   Assignment block for remixing the signal to the modulation block. Skin recognition frequencies are assigned to different M-functions.
7. Signal modulation block.
   The CDMA standard has FM4 OFM4 phase modulation.

In Denmark, the possession of the CDMA standard is the newest and most expensive, but at the same time the most recent and most expensive. The European Trade Association, within the framework of the subsequent RACE program, is developing the CODIT project, which will create one of the variants of the Universal Wireless System (UMTS) on the principle of a code line channel with a variety of broadband signals and direct spectrum extension (DS-CDMA)

The main idea of ​​the CODIT concept will be the efficiency of the frequency resource. As it was explained earlier, on a wide-range CDMA signal, the injection of a wide-range interchange is practically not indicated. Due to the power factor of the CODIT standard for data transmission, additionally, there are intervals between non-carrying frequencies.

The basic trigonometric function is described: - The number of the harmonica.

Orthogonality interval. When normalizing for tension, the base function is: Ω=2π\T

;

;
;
;

, A i - amplitude of harmonics, Θ i - phase

;

2. Distribution of signals and transfer for Volsh functions.

F-ії Walsh add up f-іy Rademacher
k = 1.2...;

sgn-signed function.

The interval is divided into 2 k intervals ∆T. The stink f-I Rademacher accepts the meaning "+1" and "-1". (The function retains its orthogonality.) wal 0 = 1 - Walsh function "0" to order 1.

Otrimannya f-ії wal larger higher orders (k = 1,2,3 ...):

1) Write down the number k in the dual system

direct code.

m-number of ranks required for filing the f-th Walshk-th order, γ i-vagovy coefficient, which can be 1 or 0 (deposit, in addition, chi no ranks are insured when summing up).

2) The number k is recoded according to the Gray code rule. With this, the youngest rank is given, the omitted code is called the Walsh code.

3) Submission f. Volsha in a row of Rodomacher:

Tse show what f. Walsh, multiplying the f-ії of Rodomacher in the singing combination with the coefficient b i . For 4kph. Walsh will be:

for tsієї the system is characterized by the expansion of f-іy in the order of growth

the number of changing signs on the interval. My system has guys

in the middle of the interval they are drawn with unpaired ones when

number of sign changes per interval for guys

change sign m/2 and unpaired (m+1)/2.

-F. Volsha in the orthogonal system.

3. Geometrical manifestation of signals and shifts.

Mathematical object A i is an element of the multiplier A 1 .

if linear operations can be performed on the object A i, then the impersonal A 1 lie on the linear space, and the iogo elements A i are the points of that space.

Expanse may be-like peace m.

If in such a space it is assigned between the points A i і A j, then the space is metric, and if it is between the cob of coordinates і be any point - the norm, and the space of norms. Vіdpovіdno norm that vіdstan can be vyznachiti. The linear normalized space is assigned the norm yak
that vіdstan
-space is called Euclidean.ifn→∞ - Hilbert space. A i - vector, iogo dozhina - norm.

In the same way U i (t) you can put a point A i or a vector in the n-worldly expanse, the roaming of some is more like the number of steps of freedom of columbing (t). Let a (t) and b (t) be expanded according to an orthogonal system of functions φ i (t).
,
Tsim kolyvannyam vіdpovіdatimut vektori
with coordinates
. Їhnya dozhina

. Taking to the mind's mind orthogonality, or rather orthonormality. Dovzhina that norm zbіgayutsya.

P a і P b - the average pet's pressure of colic. The length of the vector in the n-world expanse is determined by the effective values ​​of the floating point.

-characterize the degree of proximity. You can see it as a retail module
, The smaller the value of the time, the smaller the vіdminnostі mіzh kolivannyami.

* - The average value of the dobutku kolivan.
**-effective interaction between colivings u a іu b. Mutually tightness of coliving-P ab.
, then virazi * i ** sp_vpadut.ifu a іu b orthogonal =0.If U a =–U b then P ab = – P a = – P b . The signal that overshoot can be given as a vector. With geometric filing of coding signals. Wide-peaceful expanse in the Non-Euclidean metropolis. Vіdstany vіdstanі v tsimu space vznachaetsya for the algorithm
,n is the number of elements in the combination of the given code, and x i і y i is the value of the corresponding digits. The geometric model of the n-digit double code is the n-world cube with the edge = 1, the skin of the vertices of which represents one of the possible combinations. 000,001,010,100,101,110,011,111 Vіdstan -. Coding signal of the visual-world cube.