CN102008302A - Synthesis method of multifrequency synchronous signal source - Google Patents

Abstract

The invention discloses a synthesis method of a multifrequency synchronous signal source, comprising the following steps of, determining an amount N of main frequencies in a multifrequency synchronous signal to be synthesized, thereby determining that the signal is subdivided into 2N equal parts within a period T0, wherein N should be an odd number; finding out vectors of first N symmetric odd functions SAL (20, t), SAL (21, t), ......, SAL (2N-1, t) in a Walsh function system within a period, wherein each vector contains 2N elements; summing N vectors to obtain a sum vector g (N, t); carrying out normalization treatment on the sum vector g (N, t) with a sign function sgn () pair, thereby obtaining vectors f (N, t) of multifrequency synchronous signals of +1 and -1 within the period T0; and repeating the f (N, t) with a fundamental frequency period T0 to obtain a periodic multifrequency synchronous signal. The multifrequency synchronous signal source synthesized through the method has various very ideal time domain and frequency domain characteristics and realizes multifrequency synchronous measurement of an impedance spectroscopy.

Description

A kind of synthetic method of multi-frequency source of synchronising signal

Technical field

The invention belongs to medical electronics and test and measuring technical field, relate to a kind of synthetic method of multi-frequency source of synchronising signal.

Background technology

Bioelectrical impedance spectrum (Bioimpedance Spectroscopy is called for short BIS) technology is being with a wide range of applications aspect Human Physiology, the pathological parameter monitoring as a kind of noinvasive detection method.BIS measures and normally applies small alternating current or voltage signal by the exciting electrode that places body surface to measurand, detect the voltage or the current signal of tissue surface simultaneously by measurement electrode, calculate corresponding electrical impedance and variation thereof by measured signal, obtain relevant physiology and pathological information.This technology has cheapness, characteristics such as safe, nontoxic, easy and simple to handle, is with a wide range of applications.

Current all BIS measurement methods all belong to timesharing single-frequency measurement method in essence, and promptly the pairing physical quantity of each frequency is in different measure of time, and it is longer relatively to finish the required time of sweep measurement.But, because organism is a constantly organism of motion, the electrical impedance of biological tissue constantly changes, simultaneously when the different measuring frequency switches, newly the Time Created of bio-electrical impedance information measurement is longer under the frequency, so the data that method provided that this timesharing is measured can not accurately reflect certain electrical impedance information of organism constantly.If can be the frequency sweep time decreased, the impedance information of each Frequency point that within a short period of time is measured more can accurately reflect the actual impedance information of tested tissue.Therefore, the multi-frequency method for synchronously measuring of research BIS realizes that " instantaneous " sweep measurement of multi-frequency impedance is very significant.

One big difficult point of BIS multi-frequency synchro measure is how to produce suitable multi-frequency synchronization motivationtheory signal source.Existing in recent years scholar has carried out good try at the source of synchronising signal design aspect.For example teacher Wang Chao of University Of Tianjin has proposed to produce the different sine wave signals frequently of two-way homophase with synthetic (DDS) chip of a slice Direct Digital, realizes synchronous method by the difference amplifier then.With regard to current technology, on a slice DDS chip, realize that two paths of signals is relatively easy to synchronously, but will be more realizing between the multiple signals synchronously that different DDS chips are produced, this is to be difficult to realize or low-cost the realization on hardware.The theoretical basis of BIS technology is the Cole-Cole impedance model, and finds the solution 4 parameter (R of Cole-Cole impedance model ₀, R _∞, α, τ) need the impedance data of 4 Frequency points at least, this shows, the synchronization motivationtheory signal that only contains two Frequency points can not satisfy the requirement that follow-up data is handled, and only contains the above synchronization motivationtheory signal of 4 Frequency points and just has the actual measurement using value.

Summary of the invention

The synthetic method that the purpose of this invention is to provide a kind of multi-frequency source of synchronising signal can be used as the exciting signal source of bioelectrical impedance spectrum, electrochemical impedance spectrometry by the synthetic multi-frequency synchronizing signal of this method, realizes the multi-frequency synchro measure.

The technical solution adopted in the present invention is, a kind of synthetic method of multi-frequency source of synchronising signal is implemented according to following steps:

Step 1, at first definite number N that wants basic frequency in the synthetic multi-frequency synchronizing signal, N is necessary for odd number, determines thus at one-period T ₀Interior signal is subdivided into 2 ^NFive equilibrium;

Step 2, find out the top n symmetry odd function SAL (2 in the Walsh function system ⁰, t), SAL (2 ¹, t) ..., SAL (2 ^N-1, the t) vector in one-period, each vector comprises 2 ^NIndividual element;

Step 3, with the summation that adds up of N vector, obtain with vectorial g (N, t);

Step 4, with sign function sgn () to vectorial g (N t) carries out normalized, only got thus+1 and the multi-frequency synchronizing signal of-1 two value at one-period T ₀Interior vector f (N, t);

Step 5, (N is t) with fundamental frequency cycles T with f ₀Repeat, promptly get the multi-frequency synchronizing signal in cycle.

The synthetic multi-frequency source of synchronising signal of the inventive method, have multiple very desirable time domain and frequency domain characteristic, be suitable as very much the multi-frequency synchronization motivationtheory signal that bioelectrical impedance spectrum is measured, also can be used as the exciting signal source of electrochemical impedance spectrometry, make the multi-frequency synchro measure of impedance spectrum become possibility, have important practical value.

Description of drawings

Fig. 1 is the multi-frequency synchronizing signal synthetic schemes of the inventive method;

Fig. 2 is the symmetrical odd function SAL (2 of five in the embodiment of the invention 1 ⁰, t)～SAL (2 ⁴, t) a unified period T ₀Interior oscillogram, they are that length is 32 two-value vector;

Fig. 3 be in the embodiment of the invention 1 five symmetrical odd functions add up and vectorial g (5, signal waveforms t);

Fig. 4 be will add up in the embodiment of the invention 1 and vectorial g (5, t) gained f after the normalization (5, signal waveforms t);

Fig. 5 be the embodiment of the invention 1 gained five frequency synchronization signal f (5, amplitude spectrum t);

Fig. 6 be the embodiment of the invention 1 gained five frequency synchronization signal f (5, power spectrum t);

Fig. 7 is the symmetrical odd function SAL (2 of seven in the embodiment of the invention 2 ⁰, t)～SAL (2 ⁶, t) a unified period T ₀Interior oscillogram, they are that length is 128 two-value vector;

Fig. 8 be in the embodiment of the invention 2 seven symmetrical odd functions add up and vectorial g (7, signal waveforms t);

Fig. 9 be will add up in the embodiment of the invention 2 and vectorial g (7, t) gained f after the normalization (7, signal waveforms t);

Figure 10 be the embodiment of the invention 2 gained seven frequency synchronization signal f (7, amplitude spectrum t);

Figure 11 be the embodiment of the invention 2 gained seven frequency synchronization signal f (7, power spectrum t).

The specific embodiment

The present invention is described in detail below in conjunction with the drawings and specific embodiments.

Multi-frequency source of synchronising signal synthetic method of the present invention is based on the Walsh function theory.The Walsh function is to be proposed first in nineteen twenty-three by American scholar Joseph L.Walsh, be one in time domain [0,1] the lining value is+1 and-1 complete orthonormal function, a normalized frequency in the cycle, the Walsh function by have+1 and-1 two amplitude one be that square wave constitutes.The Walsh function has obtained extensive use in fields such as communication, signal processing, Flame Image Process, pattern recognition and spectrum measurement.The expression formula of Walsh function be WAL (n, t), wherein n represents exponent number, t is the time.Be similar to Fourier space in decomposing just, cosine function is right, the Walsh function also can use even function CAL (n, t) with odd function SAL (n t) is expressed as:

SAL(k，t)＝WAL(2k-1，t)

CAL(k，t)＝WAL(2k，t) (1)

When WAL (n, t) in the n value be 1,3,7 ..., 2 ^k-1 (k=1,2 ...) time, the Walsh function is that a series of frequencies are 2 ^K-1The square wave sequence, promptly

WAL(2 ^k-1，t)＝SAL(2 ^k-1，t)＝Sgn(sin2 ^kπt)?(2)

In the formula, Sgn (x) represents sign function:

$\mathrm{Sgn}\left(x\right)=\left\{\begin{array}{cc}1& \mathrm{forx}>0\\ 0& \mathrm{forx}=0\\ -1& \mathrm{forx}<0\end{array}\right\}---\left(3\right)$

By mistake! Do not find Reference source.An and mistake! Do not find Reference source.Formula can draw: Walsh function S AL (2 in time domain ^K-1, t) with trigonometric function sin (2 ^kπ t) the most approaching, have identical symmetry and identical frequency.Therefore, adopt simple additive operation with Walsh function S AL ( ^K-1, t) synthetic multi-frequency synchronous function:

$f(N,t)=\mathrm{Sgn}\left(\underset{k=1}{\overset{N}{\mathrm{\&Sigma;}}}\mathrm{SAL}(2^{k-1},t)\right)---\left(4\right)$

(N t) is synthetic multi-frequency synchronizing signal to f in the formula, and N is the number of main harmonic component in the synthetic waveform, and the frequency of its N main harmonic component is respectively f _k=2 ^k(k=0 ..., N-1).For fear of mistake! Do not find Reference source.Formula add the 3rd value " 0 " that occurs after the computing except that+1 and-1, promptly in order to guarantee that (N is the function of two-value (+1 and-1) t) to f, and N is necessary for odd number.

(N t) has following advantage on measuring principle: (1) signal itself contains N the main harmonic component signal that amplitude is bigger to multi-frequency synchronizing signal f; (2) amplitude of each main harmonic component is equal substantially, and the bio-electrical impedance under a plurality of main harmonic Frequency points is measured under equal accuracy, the signal to noise ratio height; (3) start-phase of each main harmonic component signal is identical, and this is very important characteristics, is very beneficial for the accurate measurement of complex impedance phase measurement; (4) frequency of each main harmonic component is by 2 ^NStepping, being evenly distributed on frequency domain helps improving the fitting precision of Cole-Cole impedance circle diagram.

As shown in Figure 1, multi-frequency synchronizing signal synthetic method of the present invention is to implement according to following steps:

Step 1, at first definite number N that wants basic frequency in the synthetic multi-frequency synchronizing signal, N is necessary for odd number, determines thus at one-period T ₀Interior signal is subdivided into 2 ^NFive equilibrium;

Step 2, find out the top n symmetry odd function SAL (2 in the Walsh function system ⁰, t), SAL (2 ¹, t) ..., SAL (2 ^N-1, the t) vector in one-period, each vector comprises 2 ^NIndividual element;

Step 3, with the summation that adds up of N vector, obtain with vectorial g (N, t);

Step 4, with sign function sgn () to vectorial g (N t) carries out normalized, only got thus+1 and the multi-frequency synchronizing signal of-1 two value at one-period T ₀Interior vector f (N, t);

Step 5, (N is t) with fundamental frequency cycles T with f ₀Repeat, promptly get the multi-frequency synchronizing signal in cycle.

Embodiment 1: according to synthesis step shown in Figure 1, synthetic five frequency synchronization signal f (5, t).

Step 1, selected N=5, hence one can see that f (5, t) at one-period T ₀Interior signal is subdivided into 32 five equilibriums.

Step 2 is found out the first five the symmetrical odd function SAL (2 in the Walsh function system ⁰, t), SAL (2 ¹, t), SAL (2 ², t), SAL (2 ³, t), SAL (2 ⁴, t), they are expressed as length is 32 two-value vector, as shown in Figure 2.

Step 3, with the summation that adds up of five vectors, obtain adding up and vectorial g (5, t), as shown in Figure 3, add up and vector is many-valued piecewise linear function.

Step 4, with sign function sgn () to add up and vectorial g (5, t) carry out normalized, can only be got thus+1 and five frequency synchronization signals of-1 two value at one-period T ₀In vector f (5, t), it in one-period, be expressed as the vector form that comprises 32 elements: f (5, t)=[1,1,1,1,1,1,1 ,-1,1,1,1 ,-1,1 ,-1 ,-1 ,-1,1,1,1 ,-1,1,-1 ,-1 ,-1,1 ,-1 ,-1 ,-1 ,-1 ,-1 ,-1 ,-1], as shown in Figure 4.

Step 5, with f (5, t) with fundamental frequency cycles T ₀Repeat, promptly get five frequency synchronization signals of cycle form.

(5, effectiveness t) is in this its spectral characteristic of utilization Fourier space analysis in order to verify composite signal f.As seen from Figure 4, (5, t), it is in period T for periodic function f ₀In limited discontinuous point, amplitude limited (+1 and-1) and signal definitely can amass, and satisfy the Dirichlet condition, according to digital signal processing theory, f (5, t) can represent with fourier series, promptly f (5, t) can be broken down into unlimited a plurality of harmonic wave:

$f(5,t)=a_0+\underset{k=1}{\overset{\&infin;}{\mathrm{\&Sigma;}}}{a}_k\cos k{\mathrm{\&omega;}}_{0}t+\underset{k=1}{\overset{\&infin;}{\mathrm{\&Sigma;}}}{b}_k\sin k{\mathrm{\&omega;}}_{0}t---\left(5\right)$

Wherein, $a_0=\frac{1}{{\mathrm{<figure-callout\; id="0"\; label="T"\; filenames="HSA00000284732000012.png,HSA00000284732000022.png"\; state="\{\{state\}\}">T</figure-callout>}}_0}{\&Integral;}_{T_0}f(5,t)\mathrm{dt}---\left(6\right)$

$a_k=\frac{2}{{\mathrm{<figure-callout\; id="0"\; label="T"\; filenames="HSA00000284732000012.png,HSA00000284732000022.png"\; state="\{\{state\}\}">T</figure-callout>}}_0}{\&Integral;}_{T_0}f(5,t)\cos k{\mathrm{\&omega;}}_0\mathrm{tdt}---\left(7\right)$

$b_k=\frac{2}{{\mathrm{<figure-callout\; id="0"\; label="T"\; filenames="HSA00000284732000012.png,HSA00000284732000022.png"\; state="\{\{state\}\}">T</figure-callout>}}_0}{\&Integral;}_{T_0}f(5,t)\sin k{\mathrm{\&omega;}}_0\mathrm{tdt}---\left(8\right)$

Simultaneously, as seen from Figure 4 f (5, t) still be odd function, and locate anti-mirror image symmetry, by the formula mistake at the intermediate point (k=16) in cycle! Do not find Reference source.An and mistake! Do not find Reference source.Calculate a ₀=0, a _k=0, a formula mistake! Do not find Reference source.Promptly be converted to:

$b_k=\frac{4}{{\mathrm{<figure-callout\; id="0"\; label="T"\; filenames="HSA00000284732000012.png,HSA00000284732000022.png"\; state="\{\{state\}\}">T</figure-callout>}}_0}{\&Integral;}_0^{{\mathrm{<figure-callout\; id="0"\; label="T"\; filenames="HSA00000284732000012.png,HSA00000284732000022.png"\; state="\{\{state\}\}">T</figure-callout>}}_0/2}f(5,t)\sin k{\mathrm{\&omega;}}_0\mathrm{tdt}---\left(9\right)$

Usually, if two-value periodic function half period [0, T ₀/ 2) inherent (0, t ₁..., t _m) m+1 discontinuous point place amplitude be+A and-A, then can be by following integral and calculating b _k:

$b_k=\frac{4}{T_0}[{\&Integral;}_0^{t_1{\mathrm{<figure-callout\; id="0"\; label="T"\; filenames="HSA00000284732000012.png,HSA00000284732000022.png"\; state="\{\{state\}\}">T</figure-callout>}}_0/2^n}A\sin k{\mathrm{\&omega;}}_0\mathrm{tdt}+{\&Integral;}_{t_1{\mathrm{<figure-callout\; id="0"\; label="T"\; filenames="HSA00000284732000012.png,HSA00000284732000022.png"\; state="\{\{state\}\}">T</figure-callout>}}_0/2^n}^{t_2{\mathrm{<figure-callout\; id="0"\; label="T"\; filenames="HSA00000284732000012.png,HSA00000284732000022.png"\; state="\{\{state\}\}">T</figure-callout>}}_0/2^n}(-A)\sin k{\mathrm{\&omega;}}_0\mathrm{tdt}+...+{\&Integral;}_{{\mathrm{<figure-callout\; id="0"\; label="t\; m\; T"\; filenames="HSA00000284732000012.png,HSA00000284732000022.png"\; state="\{\{state\}\}">t</figure-callout>}}_m{T}_{}{}_0/2^{\mathrm{<figure-callout\; id="0"\; label="n\; T"\; filenames="HSA00000284732000012.png,HSA00000284732000022.png"\; state="\{\{state\}\}">n</figure-callout>}}}^{T_{}}(-A)\sin k{\mathrm{\&omega;}}_0\mathrm{tdt}]$

$=\frac{2A}{\mathrm{k\&pi;}}[1-2\mathrm{<figure-callout\; id="1"\; label="cos\; t"\; filenames="HSA00000284732000012.png,HSA00000284732000041.png"\; state="\{\{state\}\}">cos</figure-callout>}\frac{t_{}}{}\frac{{}_1\mathrm{k\&pi;}}{2^{n-1}}+2\mathrm{<figure-callout\; id="2"\; label="cos\; t"\; filenames="HSA00000284732000012.png,HSA00000284732000022.png"\; state="\{\{state\}\}">cos</figure-callout>}\frac{t_{}}{}\frac{{}_2\mathrm{k\&pi;}}{2^{n-1}}+...-2\cos \frac{t_m\mathrm{k\&pi;}}{2^{n-1}}+\cos \mathrm{k\&pi;}]---\left(10\right)$

Among Fig. 4, (5, t) signal amplitude A=1 has 6 discontinuous points to be distributed in interior (0,7,8,11,12,13) T of half period to f ₀/ 32 places are by the formula mistake! Do not find Reference source.Can calculate f (5, fourier series coefficient t) (being frequency spectrum) b _k:

$b_k=\frac{2A}{\mathrm{k\&pi;}}[1-2\mathrm{<figure-callout\; id="7"\; label="cos"\; filenames="HSA00000284732000042.png"\; state="\{\{state\}\}">cos</figure-callout>}\frac{7\mathrm{k\&pi;}}{2^{n-1}}+2\mathrm{<figure-callout\; id="8"\; label="cos"\; filenames="HSA00000284732000012.png,HSA00000284732000022.png"\; state="\{\{state\}\}">cos</figure-callout>}\frac{8\mathrm{k\&pi;}}{2^{n-1}}-2\cos \frac{11\mathrm{k\&pi;}}{2^{n-1}}+2\mathrm{<figure-callout\; id="12"\; label="cos"\; filenames="HSA00000284732000012.png,HSA00000284732000022.png"\; state="\{\{state\}\}">cos</figure-callout>}\frac{12\mathrm{k\&pi;}}{2^{n-1}}-2\cos \frac{13\mathrm{k\&pi;}}{2^{n-1}}+\cos \mathrm{k\&pi;}]$

According to following formula can draw five frequency synchronization signal f (5, frequency spectrum t).As shown in Figure 5, be the amplitude spectrum of preceding 32 harmonic waves, obviously upwards elongation is the amplitude of 1 time, 2 times, 4 times, 8 times and 16 inferior five main harmonics successively.

According to the Pa Sewaer theorem, f (5, general power t) is:

$P=\frac{1}{{\mathrm{<figure-callout\; id="0"\; label="T"\; filenames="HSA00000284732000012.png,HSA00000284732000022.png"\; state="\{\{state\}\}">T</figure-callout>}}_0}{\&Integral;}_{{\mathrm{<figure-callout\; id="0"\; label="T"\; filenames="HSA00000284732000012.png,HSA00000284732000022.png"\; state="\{\{state\}\}">T</figure-callout>}}_0}{\left|x\left(t\right)\right|}^2\mathrm{dt}={a_0}^2+\frac{1}{2}\underset{k=1}{\overset{\&infin;}{\mathrm{\&Sigma;}}}({a_{\mathrm{<figure-callout\; id="2"\; label="k"\; filenames="HSA00000284732000012.png,HSA00000284732000022.png"\; state="\{\{state\}\}">k</figure-callout>}}}^2+{b_k}^2)=\frac{1}{2}\underset{k=1}{\overset{\&infin;}{\mathrm{\&Sigma;}}}{{\mathrm{<figure-callout\; id="2"\; label="b\; k"\; filenames="HSA00000284732000012.png,HSA00000284732000022.png"\; state="\{\{state\}\}">b</figure-callout>}}_k}^2,---\left(11\right)$

Wherein f (5, each harmonic power spectrum t) is: $P_k=\frac{1}{2}{{\mathrm{<figure-callout\; id="2"\; label="b\; k"\; filenames="HSA00000284732000012.png,HSA00000284732000022.png"\; state="\{\{state\}\}">b</figure-callout>}}_k}^2.---\left(12\right)$

According to the formula mistake! Do not find Reference source.Draw five frequency synchronization signal f (5, power spectrum t).As shown in Figure 6, be the power spectrum of preceding 32 harmonic waves, obviously upwards elongation is the power of 1 time, 2 times, 4 times, 8 times and 16 inferior five main harmonic components successively.

As previously mentioned, because the formula mistake! Do not find Reference source.Middle a ₀=0, a _k=0, five frequency synchronization signal f (5, fourier series t) is: $f(5,t)=\underset{k=1}{\overset{\&infin;}{\mathrm{\&Sigma;}}}{b}_k\sin k{\mathrm{\&omega;}}_{0}t$

(13)

Hence one can see that, f (5, t) only comprise the multifrequency sinusoid component in the signal, and the initial phase φ of each harmonic component _kBe 0 ° and (work as b _k＞0 o'clock), otherwise being 180 ° (works as b _k＜0 o'clock).As seen from Figure 5, and f (5, t) the amplitude b of five main harmonic components in the signal _kBe on the occasion of, their initial phase is 0 °.F (5, the amplitude spectrum of five main harmonic components t) and power spectrum and initial phase are as shown in table 1, by table 1 as seen, five frequency synchronization signal f (5, t) energy mainly concentrates on five main harmonic components, and these five main harmonic components have identical initial phase, are a kind of more satisfactory multi-frequency synchronizing signals.

Table 1. five frequency synchronization signal f (5, main harmonic spectral characteristic t)

Embodiment 2: according to synthesis step shown in Figure 1, synthetic seven frequency synchronization signal f (7, t).

Step 1, selected N=7, hence one can see that f (7, t) at one-period T ₀Interior signal is subdivided into 128 five equilibriums.

Step 2 is found out the first seven the symmetrical odd function SAL (2 in the Walsh function system ⁰, t), SAL (2 ¹, t), SAL (2 ², t), SAL (2 ³, t), SAL (2 ⁴, t), SAL (2 ⁵, t), SAL (2 ⁶, t), they are expressed as length is 128 two-value vector, as shown in Figure 7.

Step 3, with the summation that adds up of seven vectors, obtain adding up and vectorial g (7, t), as shown in Figure 8.As seen from Figure 8, add up and vector for many-valued piecewise linear function.

Step 4, with sign function sgn () to add up and vectorial g (7, t) carry out normalized, only got thus+1 and seven frequency synchronization signals of-1 two value at one-period T ₀In vector f (7, t), it in one-period, be expressed as the vector form that comprises 128 elements: f (7, t)=[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1 ,-1,1,1,1,1,1,1,1 ,-1,1,1,1 ,-1,1 ,-1,-1 ,-1,1,1,1,1,1,1,1 ,-1,1,1,1 ,-1,1 ,-1 ,-1 ,-1,1,1,1 ,-1,1 ,-1 ,-1 ,-1,1 ,-1 ,-1 ,-1 ,-1 ,-1 ,-1,-1,1,1,1,1,1,1,1 ,-1,1,1,1 ,-1,1 ,-1 ,-1 ,-1,1,1,1 ,-1,1,-1 ,-1 ,-1,1 ,-1 ,-1 ,-1 ,-1 ,-1 ,-1 ,-1,1,1,1 ,-1,1 ,-1 ,-1 ,-1,1 ,-1 ,-1,-1 ,-1 ,-1 ,-1 ,-1,1 ,-1 ,-1 ,-1 ,-1 ,-1,-1 ,-1 ,-1 ,-1 ,-1 ,-1 ,-1 ,-1 ,-1 ,-1], as shown in Figure 9.

Step 5, with f (7, t) with fundamental frequency cycles T ₀Repeat, promptly get seven frequency synchronization signals of cycle form.

Similar to Example 1,2 synthetic seven frequency synchronization signal f of embodiment (7, t) satisfy the Dirichlet condition equally, so f (7, t) can represent with fourier series equally.As seen from Figure 9, f (7, t) still be odd function, and locate anti-mirror image symmetry at the intermediate point (k=64) in cycle, so a ₀=0, a _k=0, again f (7, t) have 20 discontinuous points to be distributed in (0,15,16,23,24,27,28,29,32,39,40,43,44,45,48,51,52,53,56,57) T in the half period ₀/ 128 places are by the formula mistake! Do not find Reference source.Calculate f (7, frequency spectrum b t) _kThe amplitude spectrum of preceding 128 harmonic waves as shown in figure 10, obviously upwards elongation is the amplitude of 1 time, 2 times, 4 times, 8 times, 16 times, 32 times and 64 inferior seven main harmonics successively.

In like manner, according to formula (12) draw seven frequency synchronization signal f (7, power spectrum t).The power spectrum of preceding 128 harmonic waves as shown in figure 11, obviously upwards elongation is the power of 1 time, 2 times, 4 times, 8 times, 16 times, 32 times and 64 inferior seven main harmonic components successively.

(7, the amplitude spectrum of seven main harmonic components t) and power spectrum and initial phase are as shown in table 2 for f.By table 2 as seen, (7, energy t) mainly concentrates on seven main harmonic components seven frequency synchronization signal f, and these seven main harmonic components have identical initial phase, is more satisfactory multi-frequency synchronizing signal.

Table 2. seven frequency synchronization signal f (7, main harmonic spectral characteristic t)

Claims (3)

1. the synthetic method of a multi-frequency source of synchronising signal is characterized in that: implement according to following steps:

Step 1, at first definite number N that wants basic frequency in the synthetic multi-frequency synchronizing signal, N is necessary for odd number, determines thus at one-period T ₀Interior signal is subdivided into 2 ^NFive equilibrium;

Step 2, find out the top n symmetry odd function SAL (2 in the Walsh function system ⁰, t), SAL (2 ¹, t) ..., SAL (2 ^N-1, the t) vector in one-period, each vector comprises 2 ^NIndividual element;

Step 3, with the summation that adds up of N vector, obtain with vectorial g (N, t);

Step 4, with sign function sgn () to vectorial g (N t) carries out normalized, only got thus+1 and the multi-frequency synchronizing signal of-1 two value at one-period T ₀Interior vector f (N, t);

Step 5, (N is t) with fundamental frequency cycles T with f ₀Repeat, promptly get the multi-frequency synchronizing signal in cycle.

2. the synthetic method of multi-frequency source of synchronising signal according to claim 1 is characterized in that: in the step 1, when N=5, select for use five frequency synchronization signals at one-period T ₀In vector f (5, t is in one-period) be expressed as the vector form that comprises 32 elements: f (5, t)=[1,1,1,1,1,1,1 ,-1,1,1,1 ,-1,1 ,-1 ,-1 ,-1,1,1,1 ,-1,1 ,-1 ,-1 ,-1,1 ,-1 ,-1 ,-1 ,-1 ,-1 ,-1 ,-1].

3. the synthetic method of multi-frequency source of synchronising signal according to claim 1 is characterized in that: in the step 1, when N=7, select seven frequency synchronization signals for use, seven frequency synchronization signals are at one-period T ₀In vector f (7, t), in one-period, be expressed as the vector form that comprises 128 elements: f (7, t)=[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1 ,-1,1,1,1,1,1,1,1 ,-1,1,1,1 ,-1,1 ,-1 ,-1 ,-1,1,1,1,1,1,1,1 ,-1,1,1,1 ,-1,1 ,-1 ,-1 ,-1,1,1,1 ,-1,1 ,-1 ,-1 ,-1,1 ,-1 ,-1 ,-1 ,-1 ,-1 ,-1,-1,1,1,1,1,1,1,1 ,-1,1,1,1 ,-1,1 ,-1 ,-1 ,-1,1,1,1 ,-1,1 ,-1 ,-1 ,-1,1,-1 ,-1 ,-1 ,-1 ,-1 ,-1 ,-1,1,1,1 ,-1,1 ,-1,-1 ,-1,1 ,-1 ,-1 ,-1 ,-1 ,-1 ,-1 ,-1,1 ,-1 ,-1,-1 ,-1 ,-1 ,-1 ,-1 ,-1 ,-1 ,-1 ,-1 ,-1 ,-1 ,-1 ,-1].

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