Fmcw lidar system, electronic device, and method for driving lidar system

Abstract

A lidar system (10) comprising: a laser device (103) configured to emit a transmission signal (16) towards an object (15), a frequency of the transmission signal (16) being variable by varying a current injected into the laser device (103); a laser driving system (140) for driving the laser device (103); and a receiver (107) configured to receive an input signal (19), the input signal (19) being based on a superposition of the transmission signal (16) and a reflected signal (17) reflected by the object (15). The laser drive system (140) is configured to supply a current having an intensity that varies according to a plurality of different modulation modes at different timings, the modulation modes representing a change in frequency of the transmission signal (16) over time, or the intensity varies as a function of a combination of the constant current intensity and at different timings of the frequency of the transmission signal (16) over time. The speed and distance between the object (15) and the receiver (107) are configured to be determined from the input signal (19).

Description

Background Art

[0001] Tracking the pose of a device such as an AR / VR headset or controller, a robot or other mobile device is important for many applications. Odometry or simultaneous localization and mapping (SLAM) techniques are used for such tasks. These techniques link perception and movement and can utilize a variety of sensors.

[0002] FMCW (“Frequency Modulated Continuous Wave”) LiDAR (“Light Detection and Ranging”) systems, and in particular SMI LiDAR systems (“Self-Mixing Interferometry”), can measure the distance or the speed of an object. The distance provides information about the structure of the environment, while the speed provides information about the movement. Summary of the invention

[0003] The object of the present invention is to provide an improved laser radar system, an improved SLAM system, an improved electronic device, and an improved method for driving a laser radar system.

[0004] According to an embodiment, the above mentioned objects are achieved by the claimed subject matter according to the independent claims.

[0005] According to an embodiment, a laser radar system includes: a laser device configured to emit a transmission signal toward an object, the frequency of the transmission signal being variable by varying the current injected into the laser device; a laser drive system for driving the laser device; and a receiver configured to receive an input signal based on the superposition of the transmission signal and a reflection signal reflected by the object. The laser drive system is configured to supply a current having an intensity that varies according to a plurality of different modulation modes at different timings, the modulation modes representing a frequency change of the transmission signal over time, or the intensity varies according to a combination of a constant frequency and a frequency that varies over time at different timings. The speed and distance between the object and the receiver are configured to be determined based on the input signal.

[0006] According to an embodiment, the receiver may include a processing unit configured to determine the speed and distance between the object and the receiver based on the input signal. According to further embodiments, the processing unit configured to determine the speed and distance between the object and the receiver based on the input signal may be a component of a remote device, such as a controller.

[0007] For example, different modulation patterns may correspond to different triangles representing the frequency change of the transmission signal over time. Due to this particular embodiment of the laser drive system, the speed and distance between the receiver or photodetector and the object can be determined. In particular, the speed can be determined while evaluating the input signal in a frequency range that is also used to determine the distance. At the same time, ambiguities in determining the speed and distance can be reduced or avoided.

[0008] For example, the laser device may include an array of laser elements and the receiver may include an array of detector elements. Due to this configuration, the linear velocity of the receiver may be determined. For example, the processing unit may be configured to determine the linear velocity of the lidar system, for example when a sufficient number of objects are stationary and not moving.

[0009] According to an embodiment, the frequency excursion between the maximum frequency of the transmission signal and the minimum frequency of the transmission signal is from 0 to 200 GHz.

[0010] For example, at least two of the different modulation modes may correspond to triangles with different maximum frequencies of the transmission signal. According to further embodiments, at least two of the different modulation modes may correspond to triangles with different modulation periods. In this regard, the modulation periods may respectively correspond to the time distances between the minimum frequencies of the transmission signal.

[0011] According to an embodiment, the processing unit may be configured to determine a calculation result of the speed and distance between the object and the receiver from the input signal for each modulation mode. The processing unit may be further configured to determine a valid calculation result from the determined calculation result.

[0012] According to an embodiment, a simultaneous localization and mapping (SLAM) system includes the described lidar system.

[0013] Further, the electronic device may include a lidar system as described above. For example, the electronic device may be a VR / AR (“virtual reality / augmented reality”) head mounted device, for example in combination with a suitable controller, or may be a robot.

[0014] According to an embodiment, a method is suitable for driving a laser radar system, the laser radar system comprising: a laser device configured to emit a transmission signal toward an object, the frequency of the transmission signal being variable by varying a current injected into the laser device; and a receiver configured to receive an input signal based on a superposition of the transmission signal and a reflection signal reflected by the object. The method comprises supplying a current having an intensity that varies according to a plurality of different modulation patterns at different timings, the modulation patterns representing a frequency change of the transmission signal over time, or the intensity varies according to a combination of a constant frequency and a modulation pattern representing a frequency change of the transmission signal over time at different timings.

[0015] For example, at least two of the different modulation patterns correspond to triangles with different maximum frequencies of the transmission signal.

[0016] According to an embodiment, at least two of the different modulation modes correspond to triangles with different modulation periods, respectively, the modulation periods corresponding to the time distance between minimum frequencies of the transmission signal. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] The accompanying drawings are included to provide a further understanding of embodiments of the invention and are incorporated into and constitute a part of this specification. The accompanying drawings illustrate embodiments of the invention and are used together with the specification to explain the principles. Other embodiments of the invention and many expected advantages will become readily apparent as they become better understood by reference to the following detailed description. The elements of the accompanying drawings are not necessarily to scale with respect to each other. Like reference numerals designate corresponding similar parts.

[0018] Figure 1A A schematic diagram of a lidar system according to an embodiment is shown.

[0019] Figure 1B A schematic diagram of a lidar system according to a further embodiment is shown.

[0020] Figure 2A A schematic diagram of a lidar sensor that may be a component of a lidar system according to an embodiment is shown.

[0021] Figure 2B A method for determining line speed is illustrated.

[0022] Figure 3A Graphs of the transmission signal and the reflected signal in dependence on time, graphs of the beat frequency, and examples of the detection signal are shown.

[0023] FIG. 3B to FIG. 3E A waveform representing frequency changes over time is illustrated.

[0024] Figure 3F and Figure 3G A further example of a waveform of the current signal is illustrated.

[0025] Figure 4A A SLAM system according to an embodiment is shown.

[0026] Figure 4B A robot according to an embodiment is shown. DETAILED DESCRIPTION

[0027] In the following detailed description, reference is made to the accompanying drawings, which form a part of the detailed description and in which are illustrated by way of illustration specific embodiments in which the present invention may be practiced. In this regard, directional terms such as "top", "bottom", "front", "rear", "above", "on", "above", "front", "tail", etc. are used with reference to the orientation of the various figures described. Since the components of embodiments of the present invention may be positioned in many different orientations, the directional terms are used for illustrative purposes and are by no means restrictive. It should be understood that other embodiments may be utilized and structural or logical changes may be made without departing from the scope defined by the claims.

[0028] The description of the embodiments is not restrictive. In particular, elements of the embodiments described below may be combined with elements of different embodiments.

[0029] As used in this specification, the terms "coupled" and / or "electrically coupled" do not mean that it means that elements must be directly coupled together - intermediate elements may be provided between the "coupled" or "electrically coupled" elements. The term "electrically connected" is intended to describe a low-ohmic electrical connection between elements that are electrically connected together.

[0030] As used herein, the terms "having", "comprising", "including", "containing", etc. are open terms that indicate the presence of stated elements or features, but do not exclude additional elements or features. Unless the context clearly indicates otherwise, the articles "a", "an", and "the" are intended to include the plural as well as the singular.

[0031] The terms "lateral" and "horizontal" as used in this specification intend to describe an orientation parallel to a first surface of a substrate or semiconductor body. This may be, for example, the surface of a wafer or a die.

[0032] The term “vertical” as used in this specification intends to describe an orientation arranged perpendicular to a first surface of a substrate or semiconductor body.

[0033] FIG. 1 illustrates a laser radar system 10 according to an embodiment. The laser radar system 10 includes a laser device 103, which is configured to emit a transmission signal 16 toward an object 15. The frequency of the transmission signal 16 is variable by varying the current injected into the laser device 103. The system further includes a laser drive system 140 for driving the laser device 103. The laser radar system further includes a receiver 105 configured to receive an input signal. The input signal is based on the superposition of the transmission signal 16 and the reflection signal 17 that has been reflected by the object 15. The laser drive system 140 is configured to supply a current having an intensity that varies according to a plurality of different modulation modes representing the frequency change of the transmission signal over time, or varies according to a combination of the frequency change of the transmission signal over time and a constant current intensity. For example, the current may be supplied with an intensity that varies according to a plurality of different triangles representing the frequency change of the transmission signal 16 over time. According to another embodiment, the current intensity may vary according to a triangle representing the frequency change of the transmission signal 16 and a constant current intensity. The speed and distance between the object 15 and the receiver 107 may be determined according to the input signal.

[0034] According to an embodiment, the receiver 107 may include a processing unit 141 configured to determine a speed and a distance between the object 15 and the receiver 107 based on the input signal.

[0035] According to further embodiments, the received input signal or a signal generated according to the received input signal may be transmitted to a processing unit 141 which does not form a component of the lidar system 10 itself. For example, the processing unit 141 may be a component of a controller, such as a controller of a system including a VR / AR head mounted device. According to further embodiments, the processing unit 141 may be a component of a computer that controls an electronic device including the lidar system 10.

[0036] For example, the laser device 103 includes a VCSEL ("Vertical Cavity Surface Emitting Semiconductor Laser"), which is based on semiconductor materials and is configured to emit electromagnetic radiation, the wavelength of which can be changed by changing the current injected into the VCSEL. The laser drive system 140 may include a current source 149, which can be controlled to supply a current with a predetermined intensity. The receiver 107 may include a photodetector 105 configured to detect an input signal.

[0037] like Figure 1A As shown, the laser device 103 may be arranged above the photodetector 105. In more detail, for example, the photodetector 105 may be arranged on a side of the laser device 103 that is away from an emission surface of the laser device 103.

[0038] The input signal is based on a superposition of a transmission signal 16 and a reflection signal 17 reflected by an object 15. For example, the lidar sensor 20 comprising a laser device 103 and a photodetector 105 may be based on self-mixing interferometry (SMI).

[0039] According to further embodiments, the photodetector 105 may be arranged on the light emitting side of the laser device 103. Also in this case, the input signal is based on a superposition of the transmission signal 16 and the reflection signal 17.

[0040] Figure 1B A further configuration of the lidar sensor 20 and the lidar system 10 including the laser device 103 and the photodetector 105 is illustrated. As illustrated, according to an embodiment, the laser device and the photodetector 105 are not stacked, but may be arranged in a close spatial relationship in a direction perpendicular to the emission direction of the transmission signal. Figure 1B In the illustrated configuration, the reflected signal 17 is superimposed on a reference signal 18, which can be separated from the transmission beam 16, for example by means of a beam splitter or in any other arbitrary manner. Figure 1B In the illustrated embodiment, the reflected signal 17 is coherently superimposed with the reference beam, thereby achieving self-mixing interference. It is clearly understood that further configurations can be adopted that enable the reflected signal 17 to coherently superimpose with a portion of the transmitted signal 16.

[0041] Also according to Figure 2B In the illustrated embodiment, the processing unit 141 may be a component of the lidar system 10 or may be a component of a separate device.

[0042] Figure 2A An example of the configuration of the laser radar sensor 20 is shown in FIG. Figure 2A As shown, the laser device 103 includes laser elements 1041, 1042, ... 104 n According to Figure 2A In the configuration shown, the laser elements 104 are arranged along a horizontal direction or along a two-dimensional array. The transmission signal 16 emitted by the laser elements is directed to the projection lens 108, which can be used to collimate the transmission signal 16. For example, a single laser element 104 i This may be implemented at a VCSEL mounted to a suitable carrier. The individual laser elements may be electrically connected via the laser fan-out 111 to a current source 149 forming a component of the laser drive system 140 .

[0043] Figure 2A The elements shown in FIG. 1 may be arranged such that the detector elements 1061, 1062, . . . 106 nis arranged in the focal plane of the image sensor 20. The position of the focal plane can be determined by the projection lens 108. The superposition of the transmission signal 16 and the reflection signal 17 can form a single detector element 1061, 1062...106 n Received input signal 19. Detector element 1061...106 n Components forming the photodetector 105. Detector element 106 i The detector fan-out 112 may be electrically connected to the processing unit 141. In more detail, a single detector element 106 i The generated photocurrent may be processed by a processing unit 141 . Further components of the photodetector 105 and the receiver 107 may be arranged above the carrier 110 .

[0044] As will be referenced below Figure 3A As explained above, the distance and velocity of the object 15 can be determined based on the input signal. In more detail, by adopting this configuration, the radial velocity v r .

[0045] Figure 2B The radial velocity v is shown in Fig. ri The relationship between the radial velocity v and the linear velocity v. ri refers to the relationship between the sensor 20 / receiver 107, in particular the detector element 106 i The relative velocity between the object 15 in the scene projected into the direction of the ray. The index "i" designates the relative velocity between the object 15 in the scene projected into the direction of the ray. Figure 2A The corresponding laser element 104 shown in the figure i The emitted ray transmits the signal 16. When the scene is stationary, the linear velocity of the sensor is v = (v x , v y , v z ) and by each detector element 106 i The relationship between the N measured radial velocities is given by the following system of equations:

[0046]

[0047] where φ i and θ i is the angle indicating the direction of each ray. The rays may come from a single sensor array or from an arrangement of multiple sensors.

[0048] exist Figure 2B In , Cx and Cy are the coordinates of the principal point (the intersection of the optical axis and the image plane), and f is the focal length. The direction of each ray is defined by the angles φ and θ in the equation, which depend directly on the focal width and the position of each ray in the (imaginary) focal plane. These angles are determined by the calibration of the system.

[0049] Therefore, by solving this system, for example using the method of least squares or another method, the linear velocity of the sensor can be determined.

[0050] Figure 3A 1 shows a graph representing the frequency of the transmission signal 16 and the reflection signal 17 over time. Generally, in an FMCW laser radar system using the Doppler effect, an object can be detected by determining the frequency difference between the transmission signal and the reflection signal. In order to simultaneously detect the speed and distance of an object, according to Figure 3A The illustrated sawtooth or triangle shape modulates the frequency of the transmitted signal. As can be seen, the frequency of the reflected signal 17 is delayed and shifted relative to the transmitted signal 16.

[0051] Figure 3A The middle part of the graph shows the frequency difference between the two signals over time. The difference during the frequency ramp-up is labeled “f up The difference during the frequency ramp down is denoted as “f down ”. Figure 3A The lower part of shows an example of a measurement signal, which can be, for example, a voltage signal generated by the output of the photodetector 105. As can be seen, the detection signal is periodic and has a frequency corresponding to the beat signal, i.e., corresponding to the frequency difference between the transmission signal and the reflected signal 17, as shown in FIG. Figure 3A As shown in the upper part of .

[0052] In general, distance and radial velocity can be determined using the following formula:

[0053] f up =|f speed -f distonce |,

[0054] f down =|f speed +f distance |

[0055]

[0056] In the above formula, the following ranges can be assumed:

[0057] variable Typical Value <![CDATA[Distance v r > 0-10m <![CDATA[Radial velocity v r > 0-10m / s <![CDATA[Modulation frequency f mod > 100-1000Hz Frequency deviation Δf 0-200GHz Wavelength 1000nm Speed ​​of light c <![CDATA[3*10 8 m / s]]> <![CDATA[Distance contribution f to the beat frequency distance > 0-20MHz <![CDATA[Velocity contribution f to the beat frequency speed > 0-20MHz

[0058] where f mod Corresponding to 1 / T mod In general, there are three possible solutions for the distance and velocity contributions:

[0059] 1. If f speed ≥f distance :

[0060]

[0061] 2. If f distance >f speed ≥-f distance :

[0062]

[0063] 3. If -f distance >f speed :

[0064]

[0065] As indicated above, there is a range-velocity ambiguity. In more detail, there may be more than one solution to the above equation.

[0066] To address this issue, the laser driving system 140 is configured to supply current having an intensity that varies according to a plurality of different triangles representing the frequency change of the transmission signal over time, or according to a combination of a triangle representing the frequency change of the transmission signal over time and a constant current intensity.

[0067] In the following, examples of frequency-time characteristics will be explained in more detail. Figure 3B As shown, the current and therefore the frequency are modulated so that the frequency increases to a value of f0+Δf1 and then decreases to f0 at ΔT1. Thereafter, the current increases so that the frequency increases to f0+Δf2 and decreases to f0 at ΔT1+ΔT2. Using this waveform, the ambiguity can be resolved because when the system is maintained, for f mod There are two values ​​for Δf and there are two values ​​for Δf. Figure 3C A further waveform is shown, according to which the frequency first increases to a value f0+Δf1. Thereafter, the frequency decreases to f0 at ΔT1. Thereafter, the frequency increases to f0+Δf2 and then decreases to f0 at ΔT1+ΔT2. Thereafter, the frequency is at a constant value, which means that Δf=0 for t>ΔT1+ΔT2.

[0068] Figure 3D Further waveforms are shown. In particular, according to this example, ΔT2 < ΔT1 .

[0069] Figure 3E A waveform is further shown according to which the intensity varies according to a combination of a triangle representing the frequency change of the transmission signal over time and a constant current intensity. In particular, the frequency first rises to a frequency f0+Δf. Thereafter, the injected current decreases so that the frequency decreases to f0. Thereafter, the transmission signal has a constant frequency f0.

[0070] According to another embodiment, according to different modulation modes, the time at which the frequency increases from f0 to f0+Δf may be different from the time at which the frequency decreases from f0+Δf to f0. For example, for different modulation modes, f MOD Can be the same or different.

[0071] After performing a measurement, for example using the waveforms described above, the measured signal can be evaluated to eliminate solutions that result in negative distances.

[0072] According to an embodiment, when the speed contribution is close to the distance contribution or the inverse distance contribution, the beat frequency may be too small to measure, such as on an ascending or descending slope. In this case, the frequency can be set to zero as a best guess and an approximate solution for the modulation can be calculated.

[0073] According to further embodiments, due to the use of different modulation patterns, it may be possible to avoid the beat frequency being too small for the same distance-speed conditions within the range of interest.

[0074] For example, if at least two solutions determined for different modulation modes are equal to or below a given threshold, the common solution (and no approximate solution) may be averaged. If no common solution exists, the result will be considered invalid.

[0075] This will be explained in more detail using the following table:

[0076]

[0077] As shown in the table above, by using different modulation modes, the distance and radial velocity can be determined. Solution 3 with a frequency offset of 100 GHz and Solution 3 with a frequency offset of 10 GHz deliver negative distances. Therefore, these solutions are rejected. Solution 2 with a frequency offset of 100 GHz and Solution 1 with a frequency offset of 10 GHz and Solution 1 with a constant frequency deliver similar results. Therefore, a distance of 1 m and a radial velocity of 0.1 m / s are determined as the distance and velocity.

[0078] Then, before calculating the linear velocity, it is necessary to detect stationary targets as objects 15 for reflecting the transmit beam 16. Erroneous measurements corresponding to measurements of moving objects are filtered out. This can be achieved by removing measurements that deviate from the main velocity profile using known methods.

[0079] Thereafter, using the determined range and radial velocity, the linear velocity of the lidar sensor 20 may be determined.

[0080] Figure 3F and 3G Another example of a modulation mode is shown. Figure 3FAs shown, the modulation mode can be continuous. Figure 3G As further shown in FIG. 1 , the signal may be frame-based. For example, at a frame time greater than the duration of, for example, two modulation modes, two modulation modes may be measured per measurement. Thereafter, no measurement is performed until the next frame. Then, the next new modulation mode is adopted for the next frame.

[0081] Figure 4A A SLAM (Simultaneous Localization and Mapping) system according to an embodiment is shown. The SLAM system comprises a LiDAR system 10 as described above. Due to the use of the LiDAR system 10, it is possible to determine the linear velocity of the sensor. The SLAM system may comprise other sensors, such as an IMU (Inertial Measurement Unit) or a camera.

[0082] Figure 4B An electronic device 12 according to an embodiment is illustrated. The electronic device 12 includes a lidar system 10 as described herein above. Using the lidar system, the speed and distance of the electronic device 12 relative to an object can be accurately determined. For example, the electronic device 12 can be a VR / AR head-mounted device. In this case, the speed and posture of a person (such as a player wearing a VR / AR head-mounted device) can be accurately determined. In this case, the processing unit 141 can be a component of a controller, which can further, for example, control the content displayed or provided to the AR / VR head-mounted device. According to another embodiment, the electronic device 12 can be a robot.

[0083] Although embodiments of the present invention have been described above, it is apparent that other embodiments may be implemented. For example, other embodiments may include any subcombination of the features described in the claims or any subcombination of the elements described in the examples given above. Therefore, the spirit and scope of the appended claims should not be limited to the description of the embodiments contained herein.

[0084] Reference List

[0085] 10 LiDAR System

[0086] 11 SLAM System

[0087] 12 Electronic devices

[0088] 15 Objects

[0089] 16 Transmitting Signals

[0090] 17 Reflection signal

[0091] 18 Reference signal

[0092] 19 Input Signal

[0093] 20 LiDAR Sensor

[0094] 103 Laser equipment

[0095] 1041…104 n Laser components

[0096] 105 Photodetector

[0097] 1061…106 n Detector element

[0098] 107 Receiver

[0099] 108 Projection lens

[0100] 110 Carrier

[0101] 111 Laser Fan-Out

[0102] 112 Detector fan-out

[0103] 140 Laser drive system

[0104] 141 Processing Units

[0105] 149 Current Source

Claims

1. A laser radar system (10), comprising: A laser device (103) configured to emit a transmission signal (16) toward an object (15), the frequency of the transmission signal (16) being variable by varying a current injected into the laser device (103); A laser driving system (140) for driving the laser device (103); and a receiver (107) configured to receive an input signal (19) based on a superposition of the transmission signal (16) and a reflection signal (17) reflected by the object (15), wherein the laser driving system (140) is configured to supply a current having an intensity that varies according to a combination of a constant frequency and a frequency of the transmission signal (16) that varies with time at different timings, The speed and distance between the object (15) and the receiver (107) are configured to be determined based on the input signal (19).

2. The laser radar system (10) according to claim 1, The receiver (107) comprises a processing unit (141) configured to determine the speed and distance between the object (15) and the receiver (107) based on the input signal (19).

3. The laser radar system (10) according to claim 1 or 2, wherein the laser device (103) comprises laser elements (1041, 1042, ... 104 n ), and the receiver (107) includes detector elements (1061, 1062 ... 106 n ) array, wherein the processing unit (141) is configured to determine a linear velocity between the receiver (107) and the object (15).

4. A laser radar system (10) according to any one of the preceding claims, wherein a frequency offset Δf between the maximum frequency of the transmission signal and the minimum frequency of the transmission signal ranges from 0 to 200 GHz.

5. A laser radar system (10) according to any one of the preceding claims, wherein the laser drive system (140) is further configured to supply an electric current having an intensity according to a plurality of different modulation patterns at different timings, the modulation patterns representing frequency changes of the transmission signal (16) over time, and at least two of the different modulation patterns respectively correspond to triangles having different maximum frequencies of the transmission signal (16).

6. The laser radar system (10) according to claim 5, wherein at least two of the different modulation modes correspond to triangles with different modulation periods, respectively, and the modulation period corresponds to the time distance between the minimum frequencies of the transmission signal (16).

7. A lidar system (10) according to any one of claims 2 to 6, wherein the processing unit (141) is configured to determine the calculation results of the speed and distance between the object (15) and the receiver (107) according to the input signal (19) for each modulation mode, and to determine a valid calculation result based on the determined calculation result.

8. A Simultaneous Localization and Mapping (SLAM) system (11) comprising a LiDAR system (10) according to any one of the preceding claims.

9. An electronic device (12) comprising a lidar system (10) according to any one of the preceding claims.

10. The electronic device (12) according to claim 9, which is selected from an AR / VR head-mounted device and a robot.

11. A method for driving a laser radar system (10), the laser radar system (10) comprising: A laser device (103) configured to emit a transmission signal (16) toward an object (15), the frequency of the transmission signal (16) being variable by varying a current injected into the laser device (103); as well as a receiver (107) configured to receive an input signal (19) based on a superposition of the transmission signal (16) and a reflection signal (17) reflected by the object (15), The method comprises: A current is supplied, the current having a strength that varies according to a combination of a constant frequency and a frequency of the transmission signal (16) that varies with time at different timings.

12. The method according to claim 11 further comprises supplying a current having an intensity that varies according to a plurality of different modulation patterns at different timings, the different modulation patterns representing frequency changes of the transmission signal (16) over time, wherein at least two of the different modulation patterns correspond to triangles with different maximum frequencies of the transmission signal (16).

13. The method according to claim 11 or 12, wherein at least two of the different modulation patterns respectively correspond to triangles with different modulation periods, the modulation periods corresponding to the time distance between minimum frequencies of the transmission signal (16).

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