WO2009043616A1

WO2009043616A1 - Sampling method

Info

Publication number: WO2009043616A1
Application number: PCT/EP2008/059855
Authority: WO
Inventors: Matthieu Richard; Joel Bonny
Original assignee: Robert Bosch Gmbh
Priority date: 2007-09-27
Filing date: 2008-07-28
Publication date: 2009-04-09
Also published as: TW200914845A; DE102007046318A1

Abstract

The invention relates to a sampling method for determining the phase of a substantially sinusoidal signal waveform with at least a fundamental frequency which is distorted by harmonics of the fundamental frequencies, wherein a plurality of sample values are determined within one period of the signal waveform by means of sampling at a sampling frequency fS, and the phase is calculated from this, wherein the phase of at least a fundamental frequency f1 of the signal waveform and the phase of the harmonics are simultaneously determined by elimination of the harmonics situated below or above. This method permits rapid calculation of the phase position and can be easily implemented in computer systems.

Description

description

Title scanning method

State of the art

The invention relates to a sampling method for the determination of the phase of a substantially sinusoidal waveform with at least one fundamental frequency, which is distorted by harmonics of the fundamental frequencies, wherein by means of samples having a sampling frequency f _s several samples within a period of the waveform determined and from the phase is calculated ,

Such scanning methods are used, for example, in communications engineering or in interferometric measurement tasks. The so-called Nyquist-Shannon sampling theorem, or WKS sampling theorem (for Whittaker-Kotelnikow-Shannon), is a fundamental theorem in communications engineering, signal processing and information theory. The sampling theorem states that a continuous, band limited signal, with a minimum frequency of 0 Hz and a maximum frequency f _max , must be sampled with a frequency greater than 2 * f _max , so that from the discrete-time signal thus obtained the original signal without loss of information, but with infinitely great effort, reconstructed or, with finite effort, can approximate as accurately as possible. In the general case, for the sampling frequency (sampling frequency) f _s :

fs> 2 (f _max - f _min ) for f _min > 0 Hz (1)

In practice, the sampling theorem one must know or find out before sampling maximum frequency, for example by means of the Fourier analysis of a high-frequency sampled signal, and then that the signal, for example for the purpose of digitizing, with more than double Frequency must be sampled, if you want to reconstruct the signal in a good approximation. The cutoff frequency of the signal to be sampled, which can be reconstructed without error at the sampling frequency, is called Nyquist frequency f _N and corresponds to half the sampling frequency f _s .

In practice, there is often the task of equalizing distorted sinusoidal signals using harmonic harmonics by means of digital computation methods. It is therefore the object of the invention to provide a fast scanning method which on the one hand has high precision but can also be easily implemented in today's computer systems.

Disclosure of the invention

Advantages of the invention

The object is achieved by simultaneously determining the phase of at least one fundamental frequency fi of the signal profile and the phase of the harmonics by eliminating the harmonics lying below or above. An advantage of this method is that the calculation is limited to simple differences or quotient formations, which can be implemented easily and inexpensively in today's computers. Thus, a fast and relatively simple phase determination of such distorted signals can be realized.

A particularly preferred variant of the method provides that the sampling frequency f _{s is} carried out at a frequency such that a Nyquist cutoff frequency f _N , which corresponds to half the sampling frequency f _s, corresponds to at least twice the frequency of the highest harmonic to be eliminated. As a result, it can be achieved that this highest harmonic to be eliminated can be reliably detected and then the elimination method can be applied.

In this case, in a preferred variant of the method, a number of samples is selected at the sampling frequency f _s along a period of the signal curve which is smaller than the one

Number of sampling points that would be theoretically possible at the sampling frequency f _s and the time intervals between two sampling points along a period of the waveform are different, wherein the smallest time interval between two consecutive sampling points by the sampling frequency f _{s is} specified. This reduces the number of computation steps to be performed to a minimum. If, after a scan along a period of the signal course, the sampling points are displaced by a scanning displacement by the smallest time interval determined by the sampling frequency f _s and new samples are determined within the new period of the signal waveform, phase determinations can be performed at different sampling points On the one hand, they are advantageous for greater redundancy and increase the accuracy. If, in this case, the scanning shift is repeated in accordance with the number of possible sampling points at the sampling frequency f _s within a period of the signal curve and a phase average is calculated from the respectively determined phase values, the statistical error in the phase determination can thus be considerably reduced.

In a further preferred variant of the method it is provided that the phase of the fundamental frequency fi and the phase of further fundamental frequencies f ₂ , f _{3 of} the signal course are determined simultaneously by elimination calculation. This extension of the sampling method can be used particularly advantageously if the base frequency f _{2 is} assumed to be a frequency which is twice as high as the fundamental frequency fi, and the fundamental frequency f _{3 is} assumed to be three times as high as the fundamental frequency f.

If the harmonics of the fundamental frequencies are eliminated by increasing the sampling frequency f _s , a relatively simple reconstruction of distorted sinusoidal waveforms composed of a plurality of fundamental frequencies can be achieved.

In a further preferred variant of the method, it is provided that for the simultaneous determination of the phase of the fundamental frequencies, analog filters with a filter function are used, the highest permeability of which lies essentially in the frequency range of the fundamental frequencies. Thus, the quality of the phase determination can be additionally increased.

The use of the scanning method, as described above, for phase measurement, in particular in acoustic and / or optical evaluation methods, is particularly advantageous. - A -

Brief description of the drawings

The invention will be explained in more detail below with reference to an exemplary embodiment shown in the FIGURE. It shows:

FIG. 1 schematically shows the sampling method according to the prior art in the case of a sinusoidal waveform,

FIG. 2 shows the sampling method in the case of a signal waveform distorted with harmonics,

FIG. 3 shows a frequency diagram,

FIG. 4 schematically shows the scanning method according to the invention,

FIG. 5 shows another frequency diagram,

FIG. 6 schematically shows a variant of the scanning method,

FIG. 7 shows a frequency diagram with a filter function and

FIG. 8 schematically shows a transmission characteristic curve for a filter function.

Embodiments of the invention

FIG. 1 shows the sampling method in the case of a sinusoidal waveform 1, as has hitherto been conventionally used, wherein the time-varying amplitude 20 of the signal waveform 1 is shown as a function of time 10. In the example, an undistorted sine signal is shown, whose waveform 1 is determined along its period by means of equidistant samples at a sampling frequency f _s which corresponds to four times the frequency of the fundamental frequency fi 31 to be measured, one sample value Si , S ₂ , S ₃ and S ₄ 101 ... 104 and the phase φ of the waveform 1 is determined by the relationship

can be determined.

In contrast, FIG. 2 shows a distorted signal course 1 whose fundamental frequency fi 31 is distorted by superposition of a first and a second harmonic harmonic 32, 33 with the frequency 2 * f i or 3 * f i. After the evaluation, although the first harmonic 32 with the frequency 2 * fi but not the second harmonic 33 with the frequency 3 * f i can be eliminated with the sampling mode shown.

FIG. 3 shows the situation in a frequency diagram which can be determined by a Fourier analysis in which the amplitudes 20 of the discrete frequencies 30 contained in the signal course 1 are represented. In detail, these are the fundamental frequency fi 31 and the first and second harmonics 32, 33, with respect to the fundamental frequency fi 31 reduced amplitude, the frequency of which corresponds twice or three times the fundamental frequency fi. The sampling frequency f _s in the example shown corresponding to the sampling points in Figure 1 of four times the frequency to be measured fundamental frequency fi 31. Accordingly, the Nyquist cutoff frequency f _N 41 (= half sampling frequency f _s ) in the example shown equal to the frequency 2 * fi first harmonic 32, which can just be analyzed for elimination. According to the Nyquist-Shannon sampling theorem, the second harmonic 33 with the frequency 3 * fi can no longer be detected unambiguously.

FIG. 4 shows the same distorted sinusoidal waveform 1, wherein the sampling method is carried out according to the invention with a sampling frequency f _s 40, such that the Nyquist cutoff frequency f _N 41, which corresponds to half the sampling frequency f _s 40, is at least twice the frequency of the sampling frequency f _s highest to be eliminated harmonic 33 corresponds. In the example shown, the sampling frequency f _s 40 is 12 times higher than the fundamental frequency fi 31 to be measured. The Nyquist cutoff frequency f _N 41 is twice as high as the frequency of the harmonic 33 to be eliminated. The number of samples at the sampling frequency f _s 40 along a period of the waveform 1 is selected to be smaller than the number of sampling points used in the Sampling frequency f _s 40 theoretically possible. In the example shown, these are only 8 sampling points at which the sampling values S ₀ (start of period) 100, S ₂ 102, S ₃ 103, S ₅ 105, S ₆ 106, S ₈ 108, S ₉ 109 and S ₁₁ 111 are determined. The time intervals between two sampling points along the period of the signal profile 1 are different borrowed, wherein the smallest time interval of two consecutive sampling points by the sampling frequency f _s 40 is specified.

FIG. 5 shows the state of affairs according to the sampling shown in FIG. 4 in a frequency diagram.

The phase φ of the waveform 1, after elimination of the harmonics 32, 33 by the relationship

π f {S ₉ + S _n ) - {S ₃ + S ₅ ) λ

Phase® = - + aretane) - * ⁿ ') ^{3 5} ~ i (3)

3 [(S ₀ + S ₂ ) - {S ₆ + S ₈ ) J

be determined. With the sampling mode shown, the increase in complexity is only 4 additional additions, so the calculation can be easily implemented in a μ-processor. Eliminating the unwanted frequencies by means of a digital filter, on the other hand, is more complex.

FIG. 6 shows a method variant of the scanning method. After a scan along a period of the waveform 1, the sample points are shifted by a sample shift 50 by the smallest time interval determined by the sampling frequency f _s 40, respectively, and new samples 100, ..., 112 within the new period of the signal waveform 1 determined. Compared with a first sampling with the samples S ₀ (beginning of period) 100, S ₂ 102, S ₃ 103, S ₅ 105, S ₆ 106, S ₈ 108, S ₉ 109 and S ₁₁ 111 corresponding to FIG. 4, after a first sampling shift 50 Samples S ₁ 101, S ₃ 103, S ₄ 104, S ₆ 106, S ₇ 107, S ₉ 109, SlO ₉ 110 and S ₁₂ 112 determined. A phase determination for each new sample can be made with the relationship

3 12 [(Vv + S ₂ , .v) - (Vv + Vv) J where X is the number of sample shift 50.

With this method, the sampling shift 50 can be repeated in accordance with the number of possible sampling points at the sampling frequency f _s 40 within a period of the signal sequence 1 and a phase difference can be determined from the respectively determined phase values.

Average be calculated

Phases (AVG) = -? - £ Phaseφ (X) (5) nAVG X = O where n _A v _{G is} the number of phase determinations for the phase average.

In a further method example, the sampling method has been expanded with regard to a simultaneous elimination calculation for determining the phase of the fundamental frequency fi 31 and the phases of further fundamental frequencies f ₂ , f _3, 34, 37 of the signal course 1. In the example, the fundamental frequency f ₂ 34 is assumed to be a frequency twice as high as the fundamental frequency fi 31, and the fundamental frequency f ₃ 37 is assumed to be three times as high as the fundamental frequency fi 31.

The calculation of the phase of the fundamental frequency fi 31 by elimination of the fundamental frequencies f ₂ , f ₃ 34, 37 of the waveform 1 is carried out by the following equation, wherein the sampling frequency f _s 40 was 24 times higher than the lowest fundamental frequency f1:

The calculation of the phase of the fundamental frequency f ₂ 34 by elimination of the fundamental frequencies fi, f ₃ 31, 37 of the waveform 1 is carried out by the equation:

n, _{/ /} _VΛ ^π , - 2πX (\ S _{9 + X} + S _{2l + X} ) - {S _{3 + X} + S _{l5 + X} ) l Phase® (u, X) = - IV arctane -, - r - -. r (7) The calculation of the phase of the fundamental frequency f ₃ 37 by elimination of the fundamental frequencies fi, f ₂ 31, 34 of the waveform 1 is carried out by the equation:

Pha _S eφ (f ₃ , X)

(8th)

By increasing the sampling frequency f _s 40, the harmonics 32, 33, 35, 36, 38, 39 of the fundamental frequencies 31, 34, 37 can be eliminated, which corresponds to an additional improvement.

FIG. 7 shows the fundamental frequencies 31, 34, 37 as well as their harmonics 32, 33, 35, 36, 38, 39 in the frequency diagram. In addition, the Nyquist cutoff frequency f _N 41, corresponding to half the sampling frequency f _s 40 located. In order to achieve a sufficient elimination of the distortion of the signal curve 1, it is provided, for example, that a 72-fold sampling frequency f _s 40 is used in comparison to the lowest fundamental frequency 31, which is advantageous in particular for the equalization of non-pure sine signals. However, it has been shown that the fundamental frequencies fi 31 should correspond as far as possible to a pure sine function, since the first and second harmonic harmonics 32, 33 of the fundamental frequencies fi 31 influence the values of the fundamental frequencies 34, 37.

In order to improve the quality of the simultaneous phase determination of the fundamental frequencies 31, 34, 37, it is furthermore provided in the sampling method that analog filters with a filter function 60 are used whose highest permeability lies essentially in the frequency range of the fundamental frequencies 31, 34, 37. Harmonics of higher orders can thus be filtered. For an optimum compromise between the efficiency of the filter, to eliminate the higher harmonics, as well as a noise component and the response of the filter in a new measurement with changed parameters, the filter function 60 should be selected accordingly.

FIG. 8 schematically shows a typical filter function 60, wherein the logarithm of the transmission 61 is represented as a function of the logarithm of the frequency (log f) 62 is. The maximum of the filter function 60 lies in the frequency range of the fundamental frequencies 31, 34, 37.

In principle, the scanning method can also be applied to fundamental frequencies 31, 34, 37 having a fractionally rational relationship, e.g. fi, 4/3 * fi and 5/3 * fi or for example fi, 3/2 * fi and 5/2 * fi.

Claims

claims

A sampling method for determining the phase of a substantially sinusoidal waveform (1) having at least one fundamental frequency (31, 34, 37), which is defined by harmonics (32, 33, 35, 36, 38, 39) of the fundamental frequencies (31, 34 , 37) is distorted, wherein by means of samples having a sampling frequency f _s (40) a plurality of samples

(100, ..., 112) is determined within a period of the signal profile (1) and the phase is calculated therefrom, characterized in that the phase of at least one fundamental frequency fi (31) of the signal profile (1) and the phase of the harmonics (32 , 33) can be determined simultaneously by elimination of the upper or lower harmonics.

2. A sampling method according to claim 1, characterized in that the sampling frequency f _s (40) is performed at a frequency such that a Nyquist cutoff frequency f _N (41) corresponding to half the sampling frequency f _s (40), at least the twice the frequency of the highest harmonic to be eliminated (33).

3. A scanning method according to claim 1 or 2, characterized in that a number of samples at the sampling frequency f _s (40) along a period of the waveform (1) is selected, which is smaller than the number of sampling points, at the sampling frequency f _s (40) would be theoretically possible and the time intervals between two sampling points along a period of the waveform (1) are different, wherein the smallest time interval of two consecutive sampling points by the sampling frequency f _s (40) is predetermined.

4. Scanning method according to one of claims 1 to 3, characterized in that after a scan along a period of the waveform (1) the sampling points by means of a sampling shift (50) by the smallest time interval, respectively, by the sampling frequency f _s (40) is determined, shifted and new samples (100, ..., 112) are determined within the new period of the waveform (1).

5. A sampling method according to claim 4, characterized in that the sample shift (50) corresponding to the number of possible sampling points at the sampling frequency f _s (40) within a period of the waveform (1) is repeated and from the particular phase values determined a phase average is calculated.

6. Scanning method according to one of claims 1 to 5, characterized in that the phase of the fundamental frequency fi (31) and the phase of further fundamental frequencies f ₂ , f ₃ (34, 37) of the waveform (1) are determined by Eliminationsberechnung simultaneously ,

7. A sampling method according to claim 6, characterized in that as the fundamental frequency f ₂ (34) is assumed a frequency which is twice as high as the fundamental frequency fi (31), and as the fundamental frequency f ₃ (37) a threefold frequency as high as the fundamental frequency fi (31) is assumed.

8. scanning method according to one of claims 1 to 7, characterized in that by increasing the sampling frequency f _s (40), the harmonics (32, 33, 35, 36, 38, 39) of the fundamental frequencies (31, 34, 37) are eliminated ,

9. Scanning method according to one of claims 1 to 8, characterized in that for the simultaneous determination of the phase of the fundamental frequencies (31, 34, 37) analog filters with a filter function (60) are used, the highest permeability substantially in the frequency range of the fundamental frequencies ( 31, 34, 37).

10. Application of the scanning method according to one of claims 1 to 9 for phase measurement in acoustic and / or optical evaluation.