Sinelnikov Vladislav Borisovich

Introduction

Modern digital systems of transmission, voice synthesis, verification demand the work at real time scale. Algorithmic foundation of such systems construction is digital dynamic frequency analysis [1].

Research work nowelty.. Recurring inverse Fourier transform (RIFT) is a method of digital dynamic frequency analysis, that let to get the estimation of current signal spectrum at real time scale. It was developing for the needs of synthetic telephony [2]. However the absence of information on dynamic errors of current signal spectrum estimation substantively restricts the application of the method in the measuring systems.

Work object is investigation of RIFT characteristics as an instrument of current amplitude and intermittent process frequency estimation by digital modeling method.

1. Definition of investigation task

Recurring formula for Fourier coefficients computation, using in the work, proposed in [2] by R.D. Leitsom and V.N. Sobolev looks like:

where Δf=f(N) - f(0)- is a correction factor,

N - is a range,

p – is a symbolic range number

Actual and imaginary parts of Fourier coefficient are defined under the following formula: :

FT effects the computation of the DPF spectrum lines estimation in rotating reference frame, concerned with the last N counts, arranged in the register memory with cells volume [3]. Dynamic amplitude spectrum is computed under the formula:

Computational procedure of the Fourier coefficient is on the figure 1.1.

Figure 1.1. - Computational procedure of the Fourier coefficient

Discrete signal from ADC outlet goes on memory block (MB) entry and on the first adder entry. Simultaneously is carried out f(0) value pickup from MB, that goes on the second adder entry and is computed Δf value. The result from adder outlet goes on summator, where is computed the group of values Δfcosω₂, at first quarter of unit circle.

On permanent memory block (PMB) is kept necessary number of constants, placed cosω₁ and sinω₁ values in compliance with cosω₂ values [2]. With their assistance after Δfcosω₂ values computation by the commutation are generated Δfcosω₁ and Δfsinω₁ These results go further for Re_p+1(n) and J_p+1(n) values computation. On main memory blocks are kept the values of Re_p(n) and J_p(n) computation. After their pickup from MB1 and MB2 on adders A1 and A2 they are summed up respectively with Δfcosω₁ and Δfsinω₁ Obtained values are recorded at the cells, from which were read the Re_p(n) and J_p(n) values. They will be used for the computations on the next step.

2. Task solution and the results of investigation

The investigation of RIFT dynamic characteristics was holding with the assistance of programme, realized on programming language C++ 3.0. Investigated signal – is a harmonic, with frequency 1Hz, zero initial phase and unit amplitude. The dimension of running transformation window N=1024 counts. Generation process of current signal spectrum is on the figure 2.1.

On the figure 2.2. is a current spectrum of harmonic signal during phase jump on 60 degrees on 135^th count. The dimension of running transformation window N=128 counts. By the beginning of phase jump operation the process of signal spectrum assignment is completed. The process happens under the law similar to linear and completely finishes for N counts. This moment the value of nonoperating component on (120 – 150) dB less than basic component level. On 135^th count goes the phase jump at 60 degrees, that results in appearance of new transient process, with completely finishes in 128 counts after its beginning. Similar process with phase jump at 180 degrees is on the figure 2.3., with the only difference that reduction of basic component level bears greater character. From this it could be draw a conclusion that change of basic component level is depend on phase jump value.

On the figure 2.3. is a signal spectrum during serial injection of two phase jumps at 68 degrees on 135 count and at 122 degrees on 160 county. Assignment of spectrum, appropriated to physical signal is happened in N counts after the last phase jump. So, the process of spectrum forming is finished in N counts after agitation beginning, if it will not be new phase jump.

Figure 2.2 - Current spectrum of harmonic signal during phase jump on 60 degrees on 135th count.

Figure 2.3 - Current spectrum of harmonic signal during phase jump on 180 degrees on 135th count.

Figure 2.4 - Current spectrum of signal during serial injection of two phase jumps at 68 degrees on 135 count and at 122 degrees on 160 county.

At all obtained estimations of signal spectrum is a residual component that is a fatal error. Gradually they collect at the signal spectrum that could leads to the diffusion of physical process picture.

The problem of RIFT susceptibility to the influence of vibration phase change is displayed, particularly, during distinction of sampling rate from 2^k of signal spectrum maximal frequency and leads to the residual components appearance at the all frequency band, where works the analyser. This effect is on the figures 2.5 and 2.6. Thus, in the general case current signal spectrum contains the error that shoud be estimated.

Figure 2.5 - Current spectrum of harmonic signal after 1024 counts processing under the sampling rate divisible by 2^k (8Hz)

Figure 2.6 - Current spectrum of harmonic signal after 1024 counts processing under the sampling rate not divisible by 2k (7Hz)

For the estimation of calculation accuracy and determination of information pickup moment it could be applied the criterion of permissible proportion of signal and noise:

where σ_i – is a level of i component,

U_k is defined as a sum of the levels of basic component and components, lagged no more than at ± 3 frequency countsfrom basic component. This is conditioned by diffusion effect of basic frequency component in consequence of square scaled window application [4].

It was hold the investigation of γ coefficient dependence on the number of processed count. Investigated signal – is a harmonic, with frequency 1Hz, zero initial phase and unit amplitude. The dimension of running transformation window N=1024 counts. The result of investigation is on the figure 2.7. During the first N counts γ(n) grows. This corresponds to forming process of signal spectrum. After processing of N counts the relation is stabilized on the 20 dB level. From here it could be pickup of information from analyser.

Figure 2.7. - Graphic chart of proportion dependence of signal and noise on processing count number.

Conclusion

Transient process of signal spectrum formation after exposure of elementary agitation finishes in N counts of time discretization. This moment sharply decreases the level of signal spectrum transient component. But the end of spectrum computation in terminal member of iterations could be a cause of spectrum estimations errors accumulation.

The proportion of signal and noise on the analyser outlet reaches the maximum and stabilizes after the end of N counts processing that appropriates to the end of signal spectrum forming process. In future the pickup could be made at any moment with similar proportion of signal and noise. During the information pickup from analyser till the end of the spectrum formation process it should be mentioned additional error of the computation of estimated spectrum components levels and background of current spectrum.

At a point in time of report writing the master's thesis is on development stage. The further investigations will be directed on the receipt of quantitative characteristics of restoration error of harmonic components frequency of intermittent chance process and the development of estimation method of energy and frequency data of signal, invariant to the phase change.

Bibliography