DE102017101260B4 - Method for the optical comparison of the transmission properties of two transmission lines for use in motor vehicles - Google Patents

Abstract

Method for the optical measurement of the optical reflection properties of an object (O) and / or the transmission properties of a transmission path (I1, 12, 13, I4) while determining a measured value, with the steps a. Generation of a transmission signal (S9) by a first signal generator (G1), b. Transmission of a first optical signal (s1) by a first optical transmitter (H1) as a function of the first transmission signal (S9) in a first and / or second transmission path (I1, I2) and modification of the first optical signal (s1) through the passage through the first and / or second transmission path (I1, I2) to a second optical signal (s2), wherein the first and / or second transmission path (I1, I2) can contain an object (O); c. Transmission of a third optical signal (s3) by a first optical transmitter (H1) as a function of the first transmission signal (S9) in a third and / or fourth transmission path (I3, I4) and modification of the third optical signal (s3) through the passage through the third and / or fourth transmission path (I3, I4) to a fourth optical signal (s4), the third and / or fourth transmission path (I3, I4) containing an object (O) and / or a further object (O2) can; d. Receiving the second optical signal (s2) at the output of the first and / or second transmission path (I1, I2) by a first receiver (D1) and generating a first receiver output signal (S0A) as a function of the second optical signal (s2); e. Reception of the fourth optical signal (s4) at the output of the third and / or fourth transmission path (I3, I4) by a second receiver (D2) and generation of a second receiver output signal (S0B) as a function of the fourth optical signal (s4); f. Multiplication of the first receiver output signal (S0A) or a signal (S1A, S2A) dependent thereon by the transmission signal (S9) in a first multiplication device (M1A) to form a first multiplied intermediate signal (S3A); g. Multiplication of the second receiver output signal (S0B) or a signal (S1B, S2B) dependent thereon by the transmission signal (S9) in a second multiplication device (M1B) to form a second multiplied intermediate signal (S3B); h. Switching or reversing depending on a feedback signal (S8) explained later between the first multiplied intermediate signal (S3A) and the second multiplied intermediate signal (S3B) by a third multiplier (M3) to form a filter input signal (S4), this reversing also being gradual or flowing can be effected by a discrete-value or continuous-value on the one hand and a discrete-time or continuous-time feedback signal (S8) on the other hand; i. Filtering the filter input signal (S4) by a filter (F1) to form a filter output signal (S5); j. Multiplication of the filter output signal (S5) by the value (-1) by a mirroring unit (INV1), the mirroring unit (INV1) generating the feedback signal (S8). K. Output of the filter output signal (S5), the amplitude of the filter output signal (S5) representing the measured value, and / or output of the feedback signal (S8), in which case the amplitude of the feedback signal (S8) represents the measured value or a further measured value.

Description

introduction

The invention relates to a device for detecting water droplets on the windshield of a motor vehicle. For this purpose, devices are known from the prior art which evaluate the optical reflection. However, these usually have more than one light-emitting diode as a light source.

1. a. Erzeugung eines Sendesignals (S9) durch einen ersten Signalgenerator (G1),
2. b. Aussenden eines ersten optischen Signals (s1) durch einen ersten optischen Sender (H1) in Abhängigkeit von dem ersten Sendesignal (S9) in eine erste Übertragungsstrecke (I1);
3. c. Reflexion des ersten optischen Signals (s1) nach Durchlaufen der ersten Übertragungsstrecke an dem Objekt (O) als zweites optisches Signal (s2) in eine zweite Übertragungsstrecke (I2) hinein;
4. d. Gleichzeitiges Aussenden eines dritten optischen Signals (s3) durch den ersten optischen Sender (H1) in Abhängigkeit von dem ersten Sendesignal (S9) in eine dritte Übertragungsstrecke (I3);
5. e. Reflexion des dritten optischen Signals (s3) nach Durchlaufen der dritten Übertragungsstrecke (I3) an dem Objekt (O) oder einem zweiten davon beabstandeten Objekt (O2) als viertes optisches Signal (s4) in eine vierte Übertragungsstrecke (I4) hinein;
6. f. Empfang des zweiten optischen Signals (s2) am Ausgang der zweiten Übertragungsstrecke (I2) durch einen ersten Empfänger (D1) und Erzeugung eines ersten Empfängerausgangssignals (S0A) in Abhängigkeit von dem zweiten optischen Signal (s2);
7. g. Empfang des vierten optischen Signals (s4) am Ausgang der vierten Übertragungsstrecke (I4) durch einen zweiten Empfänger (D2) und Erzeugung eines zweiten Empfängerausgangssignals (S0B) in Abhängigkeit von dem vierten optischen Signal (s4).

From the DE 11 2014 000 494 T5 , of the DE 198 03 694 C1 and the EP 2 602 635 B1 a method for the optical quantitative detection of water on the windshield of a motor vehicle is known in which the optical reflection properties of an object ( O ), especially of water droplets, and / or the transmission properties of a transmission path ( I1 , I2 , I3 , I4 ) can be recorded by determining a measured value. A method that could be compiled in this way from the prior art would comprise the following steps:

1. a. Generation of a transmission signal ( S9 ) by a first signal generator ( G1 ),
2. b. Transmission of a first optical signal ( s1 ) through a first optical transmitter ( H1 ) depending on the first transmission signal ( S9 ) into a first transmission path ( I1 );
3. c. Reflection of the first optical signal ( s1 ) after passing through the first transmission path on the object ( O ) as a second optical signal ( s2 ) into a second transmission path ( I2 ) into;
4. d. Simultaneous transmission of a third optical signal (s3) by the first optical transmitter ( H1 ) depending on the first transmission signal ( S9 ) into a third transmission path ( I3 );
5. e. Reflection of the third optical signal ( s3 ) after passing through the third transmission path ( I3 ) on the object ( O ) or a second spaced apart object ( O2 ) as the fourth optical signal ( s4 ) into a fourth transmission path ( I4 ) into;
6. f. Reception of the second optical signal ( s2 ) at the output of the second transmission link ( I2 ) by a first recipient ( D1 ) and generation of a first receiver output signal (S0A) as a function of the second optical signal ( s2 );
7. G. Receipt of the fourth optical signal ( s4 ) at the output of the fourth transmission link (I4) by a second receiver ( D2 ) and generation of a second receiver output signal (S0B) as a function of the fourth optical signal ( s4 ).

The EP 2 602 635 B1 more than one LED and only has one receiver. Hence the EP 2 602 635 B1 not suitable for use with a photodiode array.

From the DE 198 03 694 C1 an image processing system is known in which two camera images are used to evaluate the wetting of the pane (see 1 , 2 of the DE 198 03 694 C1 ).

The determination of a difference image (see claim 1 of DE 198 03 694 C1 ) leads to a massive increase in hardware expenditure and thus in increased costs and energy expenditure.

That from the DE 11 2014 000 494 T5 known method works with several transmitters and a receiver and is therefore also ruled out, since the use of a single transmitter and a receiving array is not proposed. However, different measurement paths should be compared in order to obtain a measurement signal.

Object of the invention

The object of the invention is to determine a measured value as a function of the wetting of the front window of the motor vehicle.

This object is achieved by a method according to claim 1.

Description of the invention

According to the invention, it was recognized that the following method can very easily be used to determine a measured value that reflects the wetting of the front pane with water.

The generator ( G1 ) generates the transmission signal ( S9 ). A first transmitter ( H1 ) generated depending on this transmission signal ( S9 ) a first optical signal ( s1 ), which it is in a first transmission link ( I1 ) sends in. This can be approximated linearized by the following equation: $$\mathrm{<figure-callout\; id="1"\; label="s"\; filenames="DE102017101260B4\_0045.png,DE102017101260B4\_0046.png"\; state="\{\{state\}\}">s</figure-callout>}1=H_0+{\mathrm{<figure-callout\; id="1"\; label="H"\; filenames="DE102017101260B4\_0045.png,DE102017101260B4\_0046.png"\; state="\{\{state\}\}">H</figure-callout>}}_1\mathrm{S.}9$$

Ein erstes Objekt (O) reflektiert das erste optische Signal (s1) nach Austritt aus der ersten Übertragungsstrecke (I1) in eine zweite Übertragungsstrecke (I2) als zweites optisches Signal (s2) hinein.A second transmitter ( H2 ) generated depending on this transmission signal ( S9 ) a third optical signal ( s3 ), which it is in a third transmission path ( I3 ) sends in. This can be approximated linearized by the following equation: $$s3=H_0+{\mathrm{<figure-callout\; id="1"\; label="H"\; filenames="DE102017101260B4\_0045.png,DE102017101260B4\_0046.png"\; state="\{\{state\}\}">H</figure-callout>}}_1\mathrm{S.}9$$

A first object ( O ) reflects the first optical signal ( s1 ) after exiting the first transmission path ( I1 ) into a second transmission path ( I2 ) as a second optical signal ( s2 ) into it.

Ein zweites Objekt (O2) reflektiert das dritte optische Signal (s3) nach Austritt aus der dritten Übertragungsstrecke (I3) in eine vierte Übertragungsstrecke (I4) als viertes optisches Signal (s4) hinein.This can be approximated linearized by the following equation: $$\mathrm{<figure-callout\; id="2"\; label="s"\; filenames="DE102017101260B4\_0047.png"\; state="\{\{state\}\}">s</figure-callout>}2=t_0+t_1\mathrm{<figure-callout\; id="1"\; label="s"\; filenames="DE102017101260B4\_0045.png,DE102017101260B4\_0046.png"\; state="\{\{state\}\}">s</figure-callout>}1$$

A second object ( O2 ) reflects the third optical signal ( s3 ) after exiting the third transmission path ( I3 ) into a fourth transmission path ( I4 ) as the fourth optical signal ( s4 ) into it.

Hierbei nehmen wir vereinfachend an, dass die Reflexionseigenschaften des ersten Objekts (O) und zweiten Objekts (O2) übereinstimmen, ohne die Offenbarung auf diesen Fall zu beschränken. Dem Fachmann wird es ein leichtes sein, die analogen Berechnungen für den Fall ungleicher Reflexionseigenschaften der relevanten Oberflächen des ersten Objekts (O) und des zweiten Objekts (O2) durchzuführen. Auch wird dem Fachmann klar sein, dass diese Modifikationen durch die Faktoren t₀ und t₁ auch genutzt werden können, um beispielsweise ergänzend oder alternativ die Übertragungseigenschaften einer oder mehrerer Übertragungsstrecken zu beschreiben. Insgesamt können die sechs Elemente (erstes optisches Signal s1, zweites optisches Signal s2, drittes optisches Signal s3, viertes optisches Signal s4, erstes Objekt O, zweites Objekt O2) somit für die einfache Linearisierung durch 3x6=18 Parameter beschrieben werden, was hier zur Vereinfachung im Folgenden nicht berücksichtigt wird, um die Sache nicht zu verkomplizieren.This can be approximated linearized by the following equation: $$s\mathrm{4th}=t_0+t_{1}s3$$

To simplify matters, we assume that the reflection properties of the first object ( O ) and second object ( O2 ) match without restricting the disclosure to this case. It will be easy for a person skilled in the art to carry out the analog calculations for the case of unequal reflection properties of the relevant surfaces of the first object ( O ) and the second object ( O2 ). It will also be clear to the person skilled in the art that these modifications by the factors t ₀ and t _{1 can} also be used, for example to additionally or alternatively describe the transmission properties of one or more transmission links. In total, the six elements (first optical signal s1 , second optical signal s2 , third optical signal s3 , fourth optical signal s4 , first object O , second object O2) can thus be described for simple linearization by 3x6 = 18 parameters, which is not taken into account in the following for the sake of simplicity in order not to complicate matters.

The object ( O ) is typically the same as the windshield of the car with the water droplets on it.

Das vierte optische Signal (s4) tritt aus der vierten Übertragungsstrecke (I4) aus und wird durch einen zweiten Empfänger (D2) zum zweiten Empfängerausgangssignal (S0_B ) gewandelt. Die kann durch die folgende Gleichung linearisiert angenähert werden: $$S{0}_B=d_0+d_{1}s4$$

Hierbei nehmen wir wieder vereinfachend an, dass der erste Empfänger (D1) und der zweite Empfänger (D2) Linearisierungsparameter aufweisen, die sich bezüglich der Anwendung nur unwesentlich unterscheiden und damit als gleich angenommen werden können. Dem Fachmann wird es ein leichtes sein, die entsprechende Berechnung für den Fall der Ungleichheit durchzuführen.The second optical signal (s2) emerges from the second transmission path ( I2 ) and is sent by a first recipient ( D1 ) to the first receiver output signal ( S0 _A ) converted. This can be approximated linearly using the following equation: $$\mathrm{S.}{0}_{\mathrm{A.}}=d_0+d_1\mathrm{<figure-callout\; id="2"\; label="s"\; filenames="DE102017101260B4\_0047.png"\; state="\{\{state\}\}">s</figure-callout>}2$$

The fourth optical signal ( s4 ) emerges from the fourth transmission path ( I4 ) and is sent by a second recipient ( D2 ) to the second receiver output signal ( S0 _B ) converted. This can be approximated linearly using the following equation: $$\mathrm{S.}{0}_{\mathrm{B.}}=d_0+d_{1}s\mathrm{4th}$$

Here we again simplify the assumption that the first recipient ( D1 ) and the second recipient ( D2 ) Have linearization parameters that differ only insignificantly with regard to the application and can therefore be assumed to be the same. It will be easy for the person skilled in the art to carry out the corresponding calculation for the case of inequality.

This is followed by the multiplication of the first receiver output signal ( S0 _A ) or a dependent signal ( S1 _A , S2 _A ) with the transmission signal ( S9 ) in a first multiplication device ( M1 _A ) to a first multiplied intermediate signal ( S3 _A ). This can be described by the following equation: $$\mathrm{S.}{3}_{\mathrm{A.}}=\mathrm{S.}{0}_{\mathrm{A.}}\mathrm{S.}9$$

Nun wird in Abhängigkeit von einem später erläuterten Rückkopplungssignal (S8) zwischen dem ersten multiplizierten Zwischensignal (S3_A ) und dem zweiten multiplizierten Zwischensignal (S3B) durch eine dritte Multiplikationsvorrichtung (M3) umgeschaltet und hierdurch ein Filtereingangssignal (S4) gebildet. Ggf. kann dieses Umschalten abrupt durch einen Umschalter oder stufenweise oder sogar fließend erfolgen. Dieses Umschalten kann durch folgende Gleichung beschrieben werden: $$S4=S{3}_{A}S8+S{3}_B\left(1-S8\right)$$

Hierbei haben wir angenommen, dass die Maximalamplitude des Rückkopplungssignals (S8) 1 und die Minimalamplitude 0 ist.The multiplication of the second receiver output signal also follows ( S0 _B ) or a dependent signal ( S1 _B , S2 _B ) with the transmission signal ( S9 ) in a second multiplication device ( M1 _B ) to a second multiplied intermediate signal ( S3 _B ). This can be described by the following equation: $$\mathrm{S.}{3}_{\mathrm{B.}}=-\mathrm{S.}{0}_{\mathrm{B.}}\mathrm{S.}9$$

Now, depending on a feedback signal ( S8 ) between the first multiplied intermediate signal ( S3 _A ) and the second multiplied intermediate signal (S3B) by a third multiplication device ( M3 ) and thereby a filter input signal ( S4 ) educated. If necessary, this switchover can take place abruptly by means of a switch, or in stages or even fluently. This switching can be described by the following equation: $$\mathrm{S.}\mathrm{4th}=\mathrm{S.}{3}_{\mathrm{A.}}\mathrm{S.}\mathrm{8th}+\mathrm{S.}{3}_{\mathrm{B.}}\left(1-\mathrm{S.}\mathrm{8th}\right)$$

Here we have assumed that the maximum amplitude of the feedback signal ( S8 ) 1 and the minimum amplitude is 0.

Dementsprechend kann die Wirkung des Filters (F1) auf das Filtereingangssignal (S4) beschrieben werden durch die Gleichung $$S5=F\left[S4\right]$$

Dann folgt in dieser Realisierung der Erfindung die Analog-zu-Digital-Wandlung des Filterausgangssignals (S5) durch einen Analog-zu-Digital-Wandler (ADC) zu einem wertdiskreten Filterausgangssignal (S6). Hierbei entsteht ein Digitalisierungsfehler E. Daher kann dieser Schritt beschrieben werden durch: $$S6=S5\frac{E}{n}$$

Dabei gibt n die Bit-Breite des wertdiskreten Filterausgangssignals (S6) an.The next step is the filtering of the filter input signal ( S4 ) through a linear filter ( F1 ) to a filter output signal ( S5 ). A filter ( F1 ) is linear in the sense of this disclosure if the following applies to any two filter input signals A (t) and B (t) and any constant α: $$\begin{array}{c}\mathrm{F.}\left[\mathrm{A.}\left(t\right)+\mathrm{B.}\left(t\right)\right]=\mathrm{F.}\left[\mathrm{A.}\left(t\right)\right]+\mathrm{F.}\left[\mathrm{B.}\left(t\right)\right]\\ \mathrm{F.}\left[\alpha \mathrm{A.}\left(t\right)\right]=\alpha \mathrm{F.}\left[\mathrm{A.}\left(t\right)\right]\end{array}$$

Accordingly, the effect of the filter ( F1 ) on the filter input signal ( S4 ) can be described by the equation $$\mathrm{S.}5=\mathrm{F.}\left[\mathrm{S.}\mathrm{4th}\right]$$

Then follows in this implementation of the invention the analog-to-digital conversion of the filter output signal ( S5 ) through an analog-to-digital converter (ADC) to a discrete-value filter output signal ( S6 ). This results in a digitization error E. This step can therefore be described by: $$\mathrm{S.}\mathrm{6th}=\mathrm{S.}5\frac{\mathrm{E.}}{n}$$

N is the bit width of the discrete-value filter output signal ( S6 ) on.

This is followed by the synchronization of the discrete-value filter output signal ( S6 ), in particular by an associated with the transmission signal ( S9 ) clocked flip-flops ( FF ) or one with the transmission signal ( S9 ) clocked register, for the synchronized filter output signal ( S7 ). The bit width of the register depends on the bit width of the discrete-value filter output signal ( S6 ). The synchronized filter output signal ( S7 ) is thus a time-discrete signal. This is typically done with a rising and / or falling edge of the transmit signal ( S9 ).

Schließlich wird eine Multiplikation des Filterausgangssignals (S7) mit dem Wert (-1) durch eine Spiegelungseinheit (INV1) und ggf. Digital-zu-Analog-Wandlung durchgeführt, wobei die Spiegelungseinheit (INV1) das Rückkopplungssignal (S8) erzeugt.To simplify matters, we neglect the influence of this temporal discretization step and assume that it is already contained in the value E: $$\mathrm{S.}\mathrm{7th}=\mathrm{S.}\mathrm{6th}$$

Finally, a multiplication of the filter output signal ( S7 ) with the value (-1) by a mirror unit ( INV1 ) and, if necessary, digital-to-analog conversion carried out, whereby the mirroring unit ( INV1 ) the feedback signal ( S8 ) generated.

Sofern man sich nur auf Kleinsignal werte beschränkt kann hier auch $$S8=-S7$$

Verwendet werden, was zum gleichen Ergebnis führt. Es kommt also nur auf die Multiplikation des Wertes mit -1 an, die in der affinen Abbildung der vorhergehenden Formel auch enthalten ist. Die Erfindung umfasst also nicht nur die Multiplikation des absoluten Wertes von S8 mit -1, sondern auch die Multiplikation eines Kleinsignals S8 oder eines entsprechenden Signalanteils mit -1. Durch eine entsprechend hohe Verstärkung kann die Äquivalenz der vorletzten mit der letzten Gleichung hinsichtlich ihrer technischen Wirkung erreicht werden, wie im Folgenden Abschnitt ausgeführt wird.This can be described by: $$\mathrm{S.}\mathrm{8th}=\left(1-\mathrm{S.}\mathrm{7th}\right)$$

If you only limit yourself to small-signal values, you can do this here too $$\mathrm{S.}\mathrm{8th}=-\mathrm{S.}\mathrm{7th}$$

Be used, which leads to the same result. So all that matters is the multiplication of the value by -1, which is also contained in the affine mapping of the previous formula. The invention thus includes not only the multiplication of the absolute value of S8 by -1, but also the multiplication of a small signal S8 or a corresponding signal component with -1. With a correspondingly high gain, the equivalence of the penultimate equation with the last equation can be achieved with regard to their technical effect, as will be explained in the following section.

• 1. $\mathrm{<figure-callout\; id="1"\; label="s"\; filenames="DE102017101260B4\_0045.png,DE102017101260B4\_0046.png"\; state="\{\{state\}\}">s</figure-callout>}1=h_0+h_1\mathrm{<figure-callout\; id="9"\; label="S"\; filenames="DE102017101260B4\_0045.png,DE102017101260B4\_0046.png"\; state="\{\{state\}\}">S</figure-callout>}9$
  
• 2. $s3=h_0+h_1\mathrm{<figure-callout\; id="9"\; label="S"\; filenames="DE102017101260B4\_0045.png,DE102017101260B4\_0046.png"\; state="\{\{state\}\}">S</figure-callout>}9$
  
• 3. $\mathrm{<figure-callout\; id="2"\; label="s"\; filenames="DE102017101260B4\_0047.png"\; state="\{\{state\}\}">s</figure-callout>}2=t_{0A}+t_{1A}\mathrm{<figure-callout\; id="1"\; label="s"\; filenames="DE102017101260B4\_0045.png,DE102017101260B4\_0046.png"\; state="\{\{state\}\}">s</figure-callout>}1$
  
• 4. $\mathrm{<figure-callout\; id="4"\; label="s"\; filenames="DE102017101260B4\_0045.png,DE102017101260B4\_0047.png"\; state="\{\{state\}\}">s</figure-callout>}4=t_{0B}+t_{1B}s3$
  
• 5. $S{0}_A=d_0+d_1\mathrm{<figure-callout\; id="2"\; label="s"\; filenames="DE102017101260B4\_0047.png"\; state="\{\{state\}\}">s</figure-callout>}2$
  
• 6. $S{0}_B=d_0+d_1\mathrm{<figure-callout\; id="4"\; label="s"\; filenames="DE102017101260B4\_0045.png,DE102017101260B4\_0047.png"\; state="\{\{state\}\}">s</figure-callout>}4$
  
• 7. $S{3}_A=S{0}_A\mathrm{<figure-callout\; id="9"\; label="S"\; filenames="DE102017101260B4\_0045.png,DE102017101260B4\_0046.png"\; state="\{\{state\}\}">S</figure-callout>}9$
  
• 8. $S{3}_B=-S{0}_{\mathrm{<figure-callout\; id="9"\; label="B\; S"\; filenames="DE102017101260B4\_0045.png,DE102017101260B4\_0046.png"\; state="\{\{state\}\}">B</figure-callout>}}S9$
  
• 9. $\mathrm{<figure-callout\; id="4"\; label="S"\; filenames="DE102017101260B4\_0045.png,DE102017101260B4\_0047.png"\; state="\{\{state\}\}">S</figure-callout>}4=S{3}_A\mathrm{<figure-callout\; id="8"\; label="S"\; filenames="DE102017101260B4\_0047.png"\; state="\{\{state\}\}">S</figure-callout>}8+S{3}_B\left(1-S8\right)$
  
• 10. $\mathrm{<figure-callout\; id="5"\; label="S"\; filenames="DE102017101260B4\_0045.png,DE102017101260B4\_0046.png"\; state="\{\{state\}\}">S</figure-callout>}5=F\left[S4\right]$
  
• 11. $S6=\mathrm{<figure-callout\; id="5"\; label="S"\; filenames="DE102017101260B4\_0045.png,DE102017101260B4\_0046.png"\; state="\{\{state\}\}">S</figure-callout>}5+\frac{E}{n}$
  
• 12. $\mathrm{<figure-callout\; id="7"\; label="S"\; filenames="DE102017101260B4\_0046.png"\; state="\{\{state\}\}">S</figure-callout>}7=S6$
  
• 13. $\mathrm{<figure-callout\; id="8"\; label="S"\; filenames="DE102017101260B4\_0047.png"\; state="\{\{state\}\}">S</figure-callout>}8=\left(1-S7\right)$
  

The formulas are listed again here for better clarity:

• 1. $s1=H_0+H_1\mathrm{S.}9$
  
• 2. $s3=H_0+H_1\mathrm{S.}9$
  
• 3. $s2=t_{0\mathrm{A.}}+t_{1\mathrm{A.}}s1$
  
• 4th $s\mathrm{4th}=t_{0\mathrm{B.}}+t_{1\mathrm{B.}}s3$
  
• 5. $\mathrm{S.}{0}_{\mathrm{A.}}=d_0+d_{1}s2$
  
• 6th $\mathrm{S.}{0}_{\mathrm{B.}}=d_0+d_{1}s\mathrm{4th}$
  
• 7th $\mathrm{S.}{3}_{\mathrm{A.}}=\mathrm{S.}{0}_{\mathrm{A.}}\mathrm{S.}9$
  
• 8th. $\mathrm{S.}{3}_{\mathrm{B.}}=-\mathrm{S.}{0}_{\mathrm{B.}}\mathrm{S.}9$
  
• 9. $\mathrm{S.}\mathrm{4th}=\mathrm{S.}{3}_{\mathrm{A.}}\mathrm{S.}\mathrm{8th}+\mathrm{S.}{3}_{\mathrm{B.}}\left(1-\mathrm{S.}\mathrm{8th}\right)$
  
• 10. $\mathrm{S.}5=\mathrm{F.}\left[\mathrm{S.}\mathrm{4th}\right]$
  
• 11. $\mathrm{S.}\mathrm{6th}=\mathrm{S.}5+\frac{\mathrm{E.}}{n}$
  
• 12th $\mathrm{S.}\mathrm{7th}=\mathrm{S.}\mathrm{6th}$
  
• 13th $\mathrm{S.}\mathrm{8th}=\left(1-\mathrm{S.}\mathrm{7th}\right)$
  

• 1. $\mathrm{<figure-callout\; id="2"\; label="s"\; filenames="DE102017101260B4\_0047.png"\; state="\{\{state\}\}">s</figure-callout>}2=t_{0A}+t_{1A}\left(h_0+h_{1}S9\right)$
  
• 2. $\mathrm{<figure-callout\; id="4"\; label="s"\; filenames="DE102017101260B4\_0045.png,DE102017101260B4\_0047.png"\; state="\{\{state\}\}">s</figure-callout>}4=t_{0B}+t_{1B}\left(h_0+h_{1}S9\right)$
  
• 3. $S{3}_A=\left(d_0+d_{1}s2\right)\mathrm{<figure-callout\; id="9"\; label="S"\; filenames="DE102017101260B4\_0045.png,DE102017101260B4\_0046.png"\; state="\{\{state\}\}">S</figure-callout>}9$
  
• 4. $S{3}_B=\left(d_0+d_{1}s4\right)\mathrm{<figure-callout\; id="9"\; label="S"\; filenames="DE102017101260B4\_0045.png,DE102017101260B4\_0046.png"\; state="\{\{state\}\}">S</figure-callout>}9$
  
• 5. $\mathrm{<figure-callout\; id="8"\; label="S"\; filenames="DE102017101260B4\_0047.png"\; state="\{\{state\}\}">S</figure-callout>}8=1-F\left[S{3}_A+\mathrm{<figure-callout\; id="8"\; label="S"\; filenames="DE102017101260B4\_0047.png"\; state="\{\{state\}\}">S</figure-callout>}8+S{3}_B\left(1-S8\right)\right]-\frac{E}{n}$
  

Combination of equation 1 with equation 3, 2 with 4, 5 with 7, 6 with 8, 9 with 10, 10 with 11, 12 with 13 results in:

• 1. $s2=t_{0\mathrm{A.}}+t_{1\mathrm{A.}}\left(H_0+H_1\mathrm{S.}9\right)$
  
• 2. $s\mathrm{4th}=t_{0\mathrm{B.}}+t_{1\mathrm{B.}}\left(H_0+H_1\mathrm{S.}9\right)$
  
• 3. $\mathrm{S.}{3}_{\mathrm{A.}}=\left(d_0+d_{1}s2\right)\mathrm{S.}9$
  
• 4th $\mathrm{S.}{3}_{\mathrm{B.}}=\left(d_0+d_{1}s\mathrm{4th}\right)\mathrm{S.}9$
  
• 5. $\mathrm{S.}\mathrm{8th}=1-\mathrm{F.}\left[\mathrm{S.}{3}_{\mathrm{A.}}+\mathrm{S.}\mathrm{8th}+\mathrm{S.}{3}_{\mathrm{B.}}\left(1-\mathrm{S.}\mathrm{8th}\right)\right]-\frac{\mathrm{E.}}{n}$
  

Ausmultiplizieren ergibt: $$S81-F\left[\begin{array}{l}{d}_{0}S9S8+d_1{t}_{0A}S9S8+d_1{t}_{1A}{h}_{0}S9S8+d_1{t}_{1A}{h}_{1}S9S9S8\hfill \\ -d_{0}S9-d_1{t}_{0B}S9-d_1{t}_{1B}{h}_{0}S9-d_1{t}_{1B}{h}_{1}S9S9\hfill \\ +d_{0}S9S8+d_1{t}_{0B}S9S8+d_1{t}_{1B}{h}_{0}S9S8+d_1{t}_{1B}{h}_{1}S9S9S8\hfill \end{array}\right]-\frac{E}{n}$$

Dies ist gleich $$S8=1-F\left[\begin{array}{l}{d}_{0}S9\left(2S8-1\right)+d_1\left(t_{0A}+t_{0B}\right)S9S8+d_1\left(t_{1A}+t_{1B}\right)h_{0}S9S8+d_1\left(t_{1A}+t_{1B}\right)h_{1}S9S9S8\\ -d_1{t}_{0B}S9-d_1{t}_{1B}S9-d_1{t}_{1B}{h}_{1}S9S9\end{array}\right]-\frac{E}{n}$$

Der Filter wird nun so eingestellt, dass er nur Frequenzen unterhalb der Frequenz des Sendesignals S9 durchlässt.Another combination lists: $$\mathrm{S.}\mathrm{8th}=1-\mathrm{F.}\left[\left(\left(d_0+d_1\left(t_{0\mathrm{A.}}+{\mathrm{<figure-callout\; id="1"\; label="t"\; filenames="DE102017101260B4\_0045.png,DE102017101260B4\_0046.png"\; state="\{\{state\}\}">t</figure-callout>}}_{1\mathrm{A.}}\left(H_0+{\mathrm{<figure-callout\; id="1"\; label="H"\; filenames="DE102017101260B4\_0045.png,DE102017101260B4\_0046.png"\; state="\{\{state\}\}">H</figure-callout>}}_1\mathrm{S.}9\right)\right)\right)\mathrm{S.}9\right)\mathrm{S.}\mathrm{8th}+\left(-\left(d_0+d_1\left(t_{0\mathrm{A.}}+{\mathrm{<figure-callout\; id="1"\; label="t"\; filenames="DE102017101260B4\_0045.png,DE102017101260B4\_0046.png"\; state="\{\{state\}\}">t</figure-callout>}}_{1\mathrm{A.}}\left(H_0+{\mathrm{<figure-callout\; id="1"\; label="H"\; filenames="DE102017101260B4\_0045.png,DE102017101260B4\_0046.png"\; state="\{\{state\}\}">H</figure-callout>}}_1\mathrm{S.}9\right)\right)\right)\mathrm{S.}9\right)\left(1-\mathrm{S.}\mathrm{8th}\right)\right]-\frac{\mathrm{E.}}{n}$$

Multiplying out gives: $$\mathrm{S.}81-\mathrm{F.}\left[\begin{array}{l}{d}_0\mathrm{S.}9\mathrm{S.}\mathrm{8th}+d_1{t}_{0\mathrm{A.}}\mathrm{S.}9\mathrm{S.}\mathrm{8th}+d_1{\mathrm{<figure-callout\; id="1"\; label="t"\; filenames="DE102017101260B4\_0045.png,DE102017101260B4\_0046.png"\; state="\{\{state\}\}">t</figure-callout>}}_{1\mathrm{A.}}{H}_0\mathrm{S.}9\mathrm{S.}\mathrm{8th}+d_1{\mathrm{<figure-callout\; id="1"\; label="t"\; filenames="DE102017101260B4\_0045.png,DE102017101260B4\_0046.png"\; state="\{\{state\}\}">t</figure-callout>}}_{1\mathrm{<figure-callout\; id="1"\; label="A.\; H"\; filenames="DE102017101260B4\_0045.png,DE102017101260B4\_0046.png"\; state="\{\{state\}\}">A.</figure-callout>}}{H}_{}{}_1\mathrm{S.}9\mathrm{S.}9\mathrm{S.}\mathrm{8th}\hfill \\ -d_0\mathrm{S.}9-d_1{t}_{0\mathrm{B.}}\mathrm{S.}9-d_1{\mathrm{<figure-callout\; id="1"\; label="t"\; filenames="DE102017101260B4\_0045.png,DE102017101260B4\_0046.png"\; state="\{\{state\}\}">t</figure-callout>}}_{1\mathrm{B.}}{H}_0\mathrm{S.}9-d_1{\mathrm{<figure-callout\; id="1"\; label="t"\; filenames="DE102017101260B4\_0045.png,DE102017101260B4\_0046.png"\; state="\{\{state\}\}">t</figure-callout>}}_{1\mathrm{<figure-callout\; id="1"\; label="B.\; H"\; filenames="DE102017101260B4\_0045.png,DE102017101260B4\_0046.png"\; state="\{\{state\}\}">B.</figure-callout>}}{H}_{}{}_1\mathrm{S.}9\mathrm{S.}9\hfill \\ +d_0\mathrm{S.}9\mathrm{S.}\mathrm{8th}+d_1{t}_{0\mathrm{B.}}\mathrm{S.}9\mathrm{S.}\mathrm{8th}+d_1{\mathrm{<figure-callout\; id="1"\; label="t"\; filenames="DE102017101260B4\_0045.png,DE102017101260B4\_0046.png"\; state="\{\{state\}\}">t</figure-callout>}}_{1\mathrm{B.}}{H}_0\mathrm{S.}9\mathrm{S.}\mathrm{8th}+d_1{\mathrm{<figure-callout\; id="1"\; label="t"\; filenames="DE102017101260B4\_0045.png,DE102017101260B4\_0046.png"\; state="\{\{state\}\}">t</figure-callout>}}_{1\mathrm{<figure-callout\; id="1"\; label="B.\; H"\; filenames="DE102017101260B4\_0045.png,DE102017101260B4\_0046.png"\; state="\{\{state\}\}">B.</figure-callout>}}{H}_{}{}_1\mathrm{S.}9\mathrm{S.}9\mathrm{S.}\mathrm{8th}\hfill \end{array}\right]-\frac{\mathrm{E.}}{n}$$

This is the same $$\mathrm{S.}\mathrm{8th}=1-\mathrm{F.}\left[\begin{array}{l}{d}_0\mathrm{S.}9\left(2\mathrm{S.}\mathrm{8th}-1\right)+d_1\left(t_{0\mathrm{A.}}+t_{0\mathrm{B.}}\right)\mathrm{S.}9\mathrm{S.}\mathrm{8th}+d_1\left({\mathrm{<figure-callout\; id="1"\; label="t"\; filenames="DE102017101260B4\_0045.png,DE102017101260B4\_0046.png"\; state="\{\{state\}\}">t</figure-callout>}}_{1\mathrm{A.}}+{\mathrm{<figure-callout\; id="1"\; label="t"\; filenames="DE102017101260B4\_0045.png,DE102017101260B4\_0046.png"\; state="\{\{state\}\}">t</figure-callout>}}_{1\mathrm{B.}}\right)H_0\mathrm{S.}9\mathrm{S.}\mathrm{8th}+d_1\left({\mathrm{<figure-callout\; id="1"\; label="t"\; filenames="DE102017101260B4\_0045.png,DE102017101260B4\_0046.png"\; state="\{\{state\}\}">t</figure-callout>}}_{1\mathrm{A.}}+{\mathrm{<figure-callout\; id="1"\; label="t"\; filenames="DE102017101260B4\_0045.png,DE102017101260B4\_0046.png"\; state="\{\{state\}\}">t</figure-callout>}}_{1\mathrm{B.}}\right){\mathrm{<figure-callout\; id="1"\; label="H"\; filenames="DE102017101260B4\_0045.png,DE102017101260B4\_0046.png"\; state="\{\{state\}\}">H</figure-callout>}}_1\mathrm{S.}9\mathrm{S.}9\mathrm{S.}\mathrm{8th}\\ -d_1{t}_{0\mathrm{B.}}\mathrm{S.}9-d_1{\mathrm{<figure-callout\; id="1"\; label="t"\; filenames="DE102017101260B4\_0045.png,DE102017101260B4\_0046.png"\; state="\{\{state\}\}">t</figure-callout>}}_{1\mathrm{B.}}\mathrm{S.}9-d_1{\mathrm{<figure-callout\; id="1"\; label="t"\; filenames="DE102017101260B4\_0045.png,DE102017101260B4\_0046.png"\; state="\{\{state\}\}">t</figure-callout>}}_{1\mathrm{<figure-callout\; id="1"\; label="B.\; H"\; filenames="DE102017101260B4\_0045.png,DE102017101260B4\_0046.png"\; state="\{\{state\}\}">B.</figure-callout>}}{H}_{}{}_1\mathrm{S.}9\mathrm{S.}9\end{array}\right]-\frac{\mathrm{E.}}{n}$$

The filter is now set so that it only uses frequencies below the frequency of the transmitted signal S9 lets through.

Das Rückkoppelsignal S8 wird als im eingeschwungenen Zustand nahezu konstant angesehen und wird daher durchgelassen.So it applies $$0=\mathrm{F.}\left[\mathrm{S.}9\right]$$

The feedback signal S8 is considered to be almost constant in the steady state and is therefore allowed to pass.

Da das Rückkoppelsignal S8 als nahezu konstant angenommen wird, kann es vor das Filter gezogen werden. Wir erhalten: $$S8=1-d_1\left(t_{1A}+t_{1B}\right)h_{1}F\left[S9S9\right]S8+d_1{t}_{1B}{h}_{1}F\left[S9S9\right]-\frac{E}{n}$$

With this we find, simplified: $$\mathrm{S.}\mathrm{8th}=1-\mathrm{F.}\left[d_1\left({\mathrm{<figure-callout\; id="1"\; label="t"\; filenames="DE102017101260B4\_0045.png,DE102017101260B4\_0046.png"\; state="\{\{state\}\}">t</figure-callout>}}_{1\mathrm{A.}}+{\mathrm{<figure-callout\; id="1"\; label="t"\; filenames="DE102017101260B4\_0045.png,DE102017101260B4\_0046.png"\; state="\{\{state\}\}">t</figure-callout>}}_{1\mathrm{B.}}\right){\mathrm{<figure-callout\; id="1"\; label="H"\; filenames="DE102017101260B4\_0045.png,DE102017101260B4\_0046.png"\; state="\{\{state\}\}">H</figure-callout>}}_1\mathrm{S.}9\mathrm{S.}9\mathrm{S.}\mathrm{8th}-d_1{\mathrm{<figure-callout\; id="1"\; label="t"\; filenames="DE102017101260B4\_0045.png,DE102017101260B4\_0046.png"\; state="\{\{state\}\}">t</figure-callout>}}_{1\mathrm{<figure-callout\; id="1"\; label="B.\; H"\; filenames="DE102017101260B4\_0045.png,DE102017101260B4\_0046.png"\; state="\{\{state\}\}">B.</figure-callout>}}{H}_{}{}_1\mathrm{S.}9\mathrm{S.}9\right]-\frac{\mathrm{E.}}{n}$$

Because the feedback signal S8 is assumed to be almost constant, it can be drawn in front of the filter. We obtain: $$\mathrm{S.}\mathrm{8th}=1-d_1\left({\mathrm{<figure-callout\; id="1"\; label="t"\; filenames="DE102017101260B4\_0045.png,DE102017101260B4\_0046.png"\; state="\{\{state\}\}">t</figure-callout>}}_{1\mathrm{A.}}+{\mathrm{<figure-callout\; id="1"\; label="t"\; filenames="DE102017101260B4\_0045.png,DE102017101260B4\_0046.png"\; state="\{\{state\}\}">t</figure-callout>}}_{1\mathrm{B.}}\right){\mathrm{<figure-callout\; id="1"\; label="H"\; filenames="DE102017101260B4\_0045.png,DE102017101260B4\_0046.png"\; state="\{\{state\}\}">H</figure-callout>}}_1\mathrm{F.}\left[\mathrm{S.}9\mathrm{S.}9\right]\mathrm{S.}\mathrm{8th}+d_1{\mathrm{<figure-callout\; id="1"\; label="t"\; filenames="DE102017101260B4\_0045.png,DE102017101260B4\_0046.png"\; state="\{\{state\}\}">t</figure-callout>}}_{1\mathrm{<figure-callout\; id="1"\; label="B.\; H"\; filenames="DE102017101260B4\_0045.png,DE102017101260B4\_0046.png"\; state="\{\{state\}\}">B.</figure-callout>}}{H}_{}{}_1\mathrm{F.}\left[\mathrm{S.}9\mathrm{S.}9\right]-\frac{\mathrm{E.}}{n}$$

Dies kann umgeformt werden zu: $$S8=\frac{1+d_1{t}_{1B}{h}_{1}F\left[S9S9\right]}{1+d_1\left(t_{1A}+t_{1B}\right)h_{1}F\left[S9S9\right]}-\frac{E}{n\left(1+d_1\left(t_{1A}+t_{1B}\right)h_{1}F\left[S9S9\right]\right)}$$

Dies ist für sehr große h₁ oder Verstärkungen äquivalent zu $$S8\approx \frac{d_1{t}_{1B}{h}_{1}F\left[S9S9\right]}{d_1\left(t_{1A}+t_{1B}\right)h_{1}F\left[S9S9\right]}-\frac{E}{n\left(1+d_1\left(t_{1A}+t_{1B}\right)h_{1}F\left[S9S9\right]\right)}$$

Und damit zu $$S8\approx \frac{t_{1B}}{t_{1A}+t_{1B}}-\frac{E}{n\left(1+d_1\left(t_{1A}+t_{1B}\right)h_{1}F\left[S9S9\right]\right)}$$

Durch geeignete Auslegung hinsichtlich Verstärkung h₁ und Bitbreite n kann der Einfluss des Quantisierungsfehlers E minimiert werden.This can be transformed to: $$\mathrm{S.}\mathrm{8th}\left(1+d_1\left({\mathrm{<figure-callout\; id="1"\; label="t"\; filenames="DE102017101260B4\_0045.png,DE102017101260B4\_0046.png"\; state="\{\{state\}\}">t</figure-callout>}}_{1\mathrm{A.}}+{\mathrm{<figure-callout\; id="1"\; label="t"\; filenames="DE102017101260B4\_0045.png,DE102017101260B4\_0046.png"\; state="\{\{state\}\}">t</figure-callout>}}_{1\mathrm{B.}}\right){\mathrm{<figure-callout\; id="1"\; label="H"\; filenames="DE102017101260B4\_0045.png,DE102017101260B4\_0046.png"\; state="\{\{state\}\}">H</figure-callout>}}_1\mathrm{F.}\left[\mathrm{S.}9\mathrm{S.}9\right]\right)=1+d_1{\mathrm{<figure-callout\; id="1"\; label="t"\; filenames="DE102017101260B4\_0045.png,DE102017101260B4\_0046.png"\; state="\{\{state\}\}">t</figure-callout>}}_{1\mathrm{<figure-callout\; id="1"\; label="B.\; H"\; filenames="DE102017101260B4\_0045.png,DE102017101260B4\_0046.png"\; state="\{\{state\}\}">B.</figure-callout>}}{H}_{}{}_1\mathrm{F.}\left[\mathrm{S.}9\mathrm{S.}9\right]-\frac{\mathrm{E.}}{n}$$

This can be transformed to: $$\mathrm{S.}\mathrm{8th}=\frac{1+d_1{\mathrm{<figure-callout\; id="1"\; label="t"\; filenames="DE102017101260B4\_0045.png,DE102017101260B4\_0046.png"\; state="\{\{state\}\}">t</figure-callout>}}_{1\mathrm{<figure-callout\; id="1"\; label="B.\; H"\; filenames="DE102017101260B4\_0045.png,DE102017101260B4\_0046.png"\; state="\{\{state\}\}">B.</figure-callout>}}{H}_{}{}_1\mathrm{F.}\left[\mathrm{S.}9\mathrm{S.}9\right]}{1+d_1\left({\mathrm{<figure-callout\; id="1"\; label="t"\; filenames="DE102017101260B4\_0045.png,DE102017101260B4\_0046.png"\; state="\{\{state\}\}">t</figure-callout>}}_{1\mathrm{A.}}+{\mathrm{<figure-callout\; id="1"\; label="t"\; filenames="DE102017101260B4\_0045.png,DE102017101260B4\_0046.png"\; state="\{\{state\}\}">t</figure-callout>}}_{1\mathrm{B.}}\right){\mathrm{<figure-callout\; id="1"\; label="H"\; filenames="DE102017101260B4\_0045.png,DE102017101260B4\_0046.png"\; state="\{\{state\}\}">H</figure-callout>}}_1\mathrm{F.}\left[\mathrm{S.}9\mathrm{S.}9\right]}-\frac{\mathrm{E.}}{n\left(1+d_1\left({\mathrm{<figure-callout\; id="1"\; label="t"\; filenames="DE102017101260B4\_0045.png,DE102017101260B4\_0046.png"\; state="\{\{state\}\}">t</figure-callout>}}_{1\mathrm{A.}}+{\mathrm{<figure-callout\; id="1"\; label="t"\; filenames="DE102017101260B4\_0045.png,DE102017101260B4\_0046.png"\; state="\{\{state\}\}">t</figure-callout>}}_{1\mathrm{B.}}\right){\mathrm{<figure-callout\; id="1"\; label="H"\; filenames="DE102017101260B4\_0045.png,DE102017101260B4\_0046.png"\; state="\{\{state\}\}">H</figure-callout>}}_1\mathrm{F.}\left[\mathrm{S.}9\mathrm{S.}9\right]\right)}$$

This is equivalent to for very large h _{1 or gains} $$\mathrm{S.}\mathrm{8th}\approx \frac{d_1{\mathrm{<figure-callout\; id="1"\; label="t"\; filenames="DE102017101260B4\_0045.png,DE102017101260B4\_0046.png"\; state="\{\{state\}\}">t</figure-callout>}}_{1\mathrm{<figure-callout\; id="1"\; label="B.\; H"\; filenames="DE102017101260B4\_0045.png,DE102017101260B4\_0046.png"\; state="\{\{state\}\}">B.</figure-callout>}}{H}_{}{}_1\mathrm{F.}\left[\mathrm{S.}9\mathrm{S.}9\right]}{d_1\left({\mathrm{<figure-callout\; id="1"\; label="t"\; filenames="DE102017101260B4\_0045.png,DE102017101260B4\_0046.png"\; state="\{\{state\}\}">t</figure-callout>}}_{1\mathrm{A.}}+{\mathrm{<figure-callout\; id="1"\; label="t"\; filenames="DE102017101260B4\_0045.png,DE102017101260B4\_0046.png"\; state="\{\{state\}\}">t</figure-callout>}}_{1\mathrm{B.}}\right){\mathrm{<figure-callout\; id="1"\; label="H"\; filenames="DE102017101260B4\_0045.png,DE102017101260B4\_0046.png"\; state="\{\{state\}\}">H</figure-callout>}}_1\mathrm{F.}\left[\mathrm{S.}9\mathrm{S.}9\right]}-\frac{\mathrm{E.}}{n\left(1+d_1\left({\mathrm{<figure-callout\; id="1"\; label="t"\; filenames="DE102017101260B4\_0045.png,DE102017101260B4\_0046.png"\; state="\{\{state\}\}">t</figure-callout>}}_{1\mathrm{A.}}+{\mathrm{<figure-callout\; id="1"\; label="t"\; filenames="DE102017101260B4\_0045.png,DE102017101260B4\_0046.png"\; state="\{\{state\}\}">t</figure-callout>}}_{1\mathrm{B.}}\right){\mathrm{<figure-callout\; id="1"\; label="H"\; filenames="DE102017101260B4\_0045.png,DE102017101260B4\_0046.png"\; state="\{\{state\}\}">H</figure-callout>}}_1\mathrm{F.}\left[\mathrm{S.}9\mathrm{S.}9\right]\right)}$$

And with it too $$\mathrm{S.}\mathrm{8th}\approx \frac{{\mathrm{<figure-callout\; id="1"\; label="t"\; filenames="DE102017101260B4\_0045.png,DE102017101260B4\_0046.png"\; state="\{\{state\}\}">t</figure-callout>}}_{1\mathrm{<figure-callout\; id="1"\; label="B.\; t"\; filenames="DE102017101260B4\_0045.png,DE102017101260B4\_0046.png"\; state="\{\{state\}\}">B.</figure-callout>}}}{t_{}}-\frac{\mathrm{E.}}{n\left(1+d_1\left({\mathrm{<figure-callout\; id="1"\; label="t"\; filenames="DE102017101260B4\_0045.png,DE102017101260B4\_0046.png"\; state="\{\{state\}\}">t</figure-callout>}}_{1\mathrm{A.}}+{\mathrm{<figure-callout\; id="1"\; label="t"\; filenames="DE102017101260B4\_0045.png,DE102017101260B4\_0046.png"\; state="\{\{state\}\}">t</figure-callout>}}_{1\mathrm{B.}}\right){\mathrm{<figure-callout\; id="1"\; label="H"\; filenames="DE102017101260B4\_0045.png,DE102017101260B4\_0046.png"\; state="\{\{state\}\}">H</figure-callout>}}_1\mathrm{F.}\left[\mathrm{S.}9\mathrm{S.}9\right]\right)}$$

The influence of the quantization error E can be minimized through a suitable design with regard to gain h _{1 and bit width n.}

Die Vorrichtung ist also geeignet, den relativen Anteil des vom Objekt (O) über die dritte Übertragungsstrecke (I3) und die vierte Übertragungsstrecke (I4) erhaltenen optischen Signals am gesamten optischen Signal in Form des synchronisierten Filterausgangssignals (S7) zu ermitteln.The relationship remains for the case of a sufficiently large signal amplitude $$\mathrm{S.}\mathrm{8th}\approx \frac{{\mathrm{<figure-callout\; id="1"\; label="t"\; filenames="DE102017101260B4\_0045.png,DE102017101260B4\_0046.png"\; state="\{\{state\}\}">t</figure-callout>}}_{1\mathrm{<figure-callout\; id="1"\; label="B.\; t"\; filenames="DE102017101260B4\_0045.png,DE102017101260B4\_0046.png"\; state="\{\{state\}\}">B.</figure-callout>}}}{t_{}}$$

The device is therefore suitable for determining the relative proportion of the O ) over the third transmission path ( I3 ) and the fourth transmission path ( I4 ) optical signal obtained on the entire optical signal in the form of the synchronized filter output signal ( S7 ) to investigate.

It is obvious to the person skilled in the art that discretization (digitization) in terms of time and value is not absolutely necessary and can take place at different points in the signal path. It is also conceivable to carry out the digitization directly in the receiving elements and to carry out the entire following signal path in digitized form. The signals can therefore also be understood as variable values of a program that is executed in a signal processor.

If necessary, the filter output signal ( S5 ) can be multiplied by -1 and used directly as a feedback signal ( S8 ) be used. In this case the third multiplier ( M3 ) be able to use this feedback signal ( S8 ) to process. In that case the filter output signal ( S5 ) is used as a measured value instead of the synchronized filter output signal.

Filtering the filter input signal ( S4 ) through the filter ( F1 ) to a filter output signal ( S5 ) is preferably carried out by low-pass filtering with a cut-off frequency f _g , whereby the low-pass filter can also be an integrator. In order for the filter conditions that were explained above to apply, the transmit signal ( S9 ) a transmission signal with a lower limit frequency f _u and the following applies to the amounts of these limit frequencies: f _g < f _u .

Figure list

• 1 shows the signal scheme of a device according to the invention with a switch as a third multiplier M3
• 2 shows the signal scheme of a device according to the invention with an n-bit-wide feedback signal ( S8 ) to control the third multiplier M3

List of reference symbols

D1

first recipient

D2

second recipient

G1

Signal generator

H1

first sender

H2

second transmitter

F1

Filter, preferably a low-pass filter with a cutoff frequency f _g or an integrator

f _g

Cutoff frequency of the low-pass filter (filter F1 )

f _u

lower limit frequency of the transmission signal ( S9 ).

f _o

upper limit frequency of the transmission signal ( S9 ). The upper limit frequency is preferred f _o less than twice the lower limit frequency f _u .

FF

Synchronizing device, preferably a flip-flop. In the case of an n-bit-wide discrete-value filter output signal ( S6 ) it can also be a register, for example made up of several flip-flops.

I1

first transmission path

I2

second transmission path

I3

third transmission path

I4

fourth transmission path

INV1

Mirroring unit, preferably an inverter

M1 _A

first multiplier

M1 _B

second multiplier

M3

third multiplication device for switching (if implemented as a switch) or stepwise or continuous reversing between the first multiplied intermediate signal ( S3 _A ) and the second multiplied intermediate signal ( S3 _B ) to generate a filter input signal ( S4 ), whereby the term switching here includes all types of reversing with a strictly monotonic dependence function of the components of the first multiplied intermediate signal ( S3 _A ) and the second multiplied intermediate signal ( S3 _B ) at the filter input signal ( S4 ) depending on the feedback signal ( S8 ) includes. The so broadly understood switching takes place as a function of the said feedback signal ( S8 ). The realization of a one-bit-wide digital feedback signal ( S8 ) controlled switch (for example a transfer gate) is particularly preferred.

O

Object (e.g. windshield with water droplets)

O2

possibly second object

S0 _A

first receiver output signal

S0 _B

second receiver output signal

s1

first optical signal

S1 _A

first input amplifier output signal

S1 _B

second input amplifier output signal

s2

second optical signal

S2 _A

first input filter output signal

S2 _B

second input filter output signal

s3

third optical signal

S3 _A

first multiplied intermediate signal

S3 _B

second multiplied intermediate signal

s4

fourth optical signal

S4

Filter input signal

S5

Filter output signal (This reflects a possible measured value.)

S6

Discrete-value filter output signal (This reflects a possible measured value.) The discrete-value filter output signal is typically, but not necessarily, continuous in time.

S7

synchronized filter output signal (This reflects a possible measured value.) The synchronized filter output signal is typically discrete in value and time.

S8

Feedback signal (This reflects a possible measured value.)

S9

Transmission signal. The transmission signal is preferably mono-frequency or band-limited with a lower limit frequency in terms of magnitude f _u and an upper limit frequency in terms of magnitude f _o . The following preferably applies to the amounts of these limit frequencies: (| f ₀ -f _u |) <| f _g | <| f _u |. It is preferably a PWM signal with a 50% duty cycle. The use of PCM signals is possible. In this case, however, care must be taken that the synchronization in the flip-flop ( FF ) only ever occurs at the end of a PCM code. The PCM code should have a fill factor of 50%. This is the temporal 1 area compared to the temporal 0 area based on the duration of the transmission of the PCM code in question. The use of band-limited random signals is also possible. In this case, a low-pass filter similar to the filter ( F1 ) which filters the square of the transmitted signal and subtracts the mean amplitude. Synchronization can then take place at the zero crossings of the signal which then follow. In a similar way, PFM modulation methods etc. can be used if the synchronization in the synchronization device only takes place if the amount of light emitted per unit of time up to that point corresponds to the target value, typically 50%.

Claims (4)

Method for the optical measurement of the optical reflection properties of an object (O) and / or the transmission properties of a transmission path (I1, 12, 13, I4) while determining a measured value, with the steps a. Generation of a transmission signal (S9) by a first signal generator (G1), b. Transmission of a first optical signal (s1) by a first optical transmitter (H1) as a function of the first transmission signal (S9) in a first and / or second transmission path (I1, I2) and modification of the first optical signal (s1) through the passage through the first and / or second transmission path (I1, I2) to a second optical signal (s2), wherein the first and / or second transmission path (I1, I2) can contain an object (O); c. Transmission of a third optical signal (s3) by a first optical transmitter (H1) as a function of the first transmission signal (S9) in a third and / or fourth transmission path (I3, I4) and modification of the third optical signal (s3) through the passage through the third and / or fourth transmission path (I3, I4) to a fourth optical signal (s4), the third and / or fourth transmission path (I3, I4) containing an object (O) and / or a further object (O2) can; d. Receiving the second optical signal (s2) at the output of the first and / or second transmission path (I1, I2) by a first receiver (D1) and generating a first receiver output _{signal (S0 A} ) as a function of the second optical signal (s2); e. Receiving the fourth optical signal (s4) at the output of the third and / or fourth transmission path (I3, I4) by a second receiver (D2) and generating a second receiver output _{signal (S0 B} ) as a function of the fourth optical signal (s4); f. multiplication of the first receiver output _{signal (S0 A} ) or a signal (S1 _A , S2 _A ) dependent thereon by the transmission signal (S9) in a first multiplication device (M1 _A ) to form a first multiplied intermediate signal (S3 _A ); G. Multiplication of the second receiver output _{signal (S0 B} ) or a signal (S1 _B , S2 _B ) dependent thereon by the transmission signal (S9) in a second multiplication device (M1 _B ) to form a second multiplied intermediate signal (S3 _B ); H. Switching or reversing depending on a feedback signal (S8) explained later between the first multiplied intermediate signal (S3 _A ) and the second multiplied intermediate signal (S3B) by a third multiplier (M3) to form a filter input signal (S4), this reversing also in stages or can be effected in a flowing manner by means of a discrete-value or continuous-value on the one hand and a discrete-time or continuous-time feedback signal (S8) on the other; i. Filtering the filter input signal (S4) by a filter (F1) to form a filter output signal (S5); j. Multiplication of the filter output signal (S5) by the value (-1) by a mirroring unit (INV1), the mirroring unit (INV1) generating the feedback signal (S8). k. Output of the filter output signal (S5), the amplitude of the filter output signal (S5) representing the measured value, and / or output of the feedback signal (S8), in which case the amplitude of the feedback signal (S8) represents the measured value or a further measured value. Procedure according to Claim 1 comprising the additional steps a. Analog-to-digital conversion of the filter output signal (S5) by an analog-to-digital converter to form a discrete-value filter output signal (S6); b. Synchronizing the discrete-value filter output signal (S6), which can be done by a flip-flop (FF) clocked with the transmit signal (S9) or a register clocked with the transmit signal (S9), to the synchronized filter output signal (S7); c. Multiplication of the synchronized filter output signal (S7) instead of the filter output signal (S5) by the value (-1) by a mirroring unit (INV1), the mirroring unit (INV1) generating the feedback signal (S8). d. Edition i. the synchronized filter output signal (S7) instead of the filter output signal (S5), the amplitude of the synchronized filter output signal (S7) representing the measured value or a further measured value instead of the filter output signal (S5) and / or ii. of the feedback signal (S8) instead of the filter output signal (S5), the amplitude of the feedback signal (S8) representing the measured value or a further measured value instead of the filter output signal (S5). Procedure according to Claim 1 or 2 characterized by a. that the filtering of the filter input signal (S4) by a filter (F1) to a filter output signal (S5) is an integration. Procedure according to Claim 1 or 2 characterized by a. that the filtering of the filter input signal (S4) by a filter (F1) to a filter output signal (S5) is a low-pass filtering with a cutoff frequency f _g and b. that the transmission signal (S9) is a transmission signal with a lower limit frequency f _u and with an upper limit frequency f _o and c. that the following applies to the amounts of these limit frequencies: (| f ₀ -f _u |) <| f _g | <| f _u |;

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