A Design Method of Pulse Control Signal Based on LiDAR Target Point Cloud

Abstract

The present invention discloses a method for designing a pulse control signal based on the target point cloud of a lidar. The method includes the following steps: 1. The point cloud collected by the target lidar is used as the template point cloud; 2. Data preprocessing is performed on the collected template point cloud to obtain the time from the emission to the reception of the laser pulse corresponding to the target lidar, the lidar beam number information of the template point cloud, and the working cycle number information; 3. According to the time from the emission to the reception of the laser pulse of the target lidar, the lidar beam number information of the template point cloud, and the working cycle number information, a pulse control signal for the target lidar is designed to control the target lidar to generate the same point cloud as the template point cloud. The present invention can generate point clouds that do not exist in the actual environment but can be received and processed by the lidar, providing a theoretical basis for the realization of adversarial simulation for lidars and guaranteeing the subsequent analysis and improvement of the safety performance of lidars.

Description

Technical Field

[0001] The present invention belongs to a method for designing a pulse control signal of a lidar in the fields of lidar safety and laser pulse coding and electronic control of a laser, and particularly relates to a method for designing a pulse control signal based on lidar target point cloud. Background Art

[0002] A lidar is an important active remote sensing sensor. Its working principle is to emit a laser beam towards a target as a detection signal, then receive the signal reflected from the target, analyze the time required for the laser to complete a round trip between the sensor and the target, calculate the relative distance between the detected target and the lidar, and after appropriate processing, the spatial information of the target can be obtained. The lidar can penetrate the occlusion of obstacles and directly obtain high-precision three-dimensional information of the actual detected object for identifying, classifying, and tracking moving objects.

[0003] The lidar continuously rotates the emitting head to change the fast and accurately emitted laser from a "line" to a "plane", and arranges multiple laser beams in the numerical direction to form multiple planes, achieving the purpose of dynamic scanning and receiving information. Since the emitters of the multi-line lidar have a consistent and stable pulse frequency, and the detection distance and angular resolution are consistent, the state of the object in the actual situation can be predicted through the point cloud information.

[0004] The real lidar point cloud needs to receive the target echo to be generated, so it needs to satisfy a basic rule: points only exist on the laser beam of the lidar, and each beam only represents one point during each emission. This rule provides a theoretical basis for the realization of adversarial simulation for lidar, but existing experiments of injecting point cloud signals into the lidar to form interference or deception cannot be realized under actual conditions, and the added point cloud is often chaotic, thus unable to simulate the point cloud state of the real environment to the greatest extent. Summary of the Invention

[0005] In order to solve the problems existing in the background art, the present invention provides a method for designing a pulse control signal based on lidar target point cloud, which can generate pulse control signals with precise coding, variable interval coding, and variable pulse coding, thereby modulating the emitted point cloud output by the lidar. The present invention can use a lidar of the same model to collect the point cloud existing in the actual environment as a template point cloud, design the pulse control signal of the lidar according to the information of the template point cloud, and inject it into the working lidar through hardware such as a laser, so that the lidar can still receive the same point cloud signal as the template point cloud at a time or space where the template does not exist. This provides a theoretical basis for the realization of laser deception interference experiments for lidar and guarantees the subsequent analysis and improvement of the safety performance of lidar.

[0006] The technical solution of the present invention is as follows:

[0007] The present invention includes the following steps:

[0008] Step 1: The point cloud collected by the target lidar is used as the template point cloud;

[0009] Step 2: Perform data preprocessing on the collected template point cloud to obtain the time from the emission to the reception of the laser pulse corresponding to the target lidar, the lidar beam number information of the template point cloud, and the working cycle number information;

[0010] Step 3: Design a pulse control signal for the target lidar according to the time from the emission to the reception of the laser pulse of the target lidar, the lidar beam number information of the emitted point cloud, and the working cycle number information, so as to control the target lidar to generate the same point cloud as the template point cloud.

[0011] The specific content of Step 2 is as follows:

[0012] 2.1) Convert the spatial position coordinate information of the collected template point cloud into three-dimensional polar coordinate information to obtain the relative distance information between the template point cloud and the target lidar, the vertical angle information of the template point cloud, and the horizontal angle information;

[0013] 2.2) Calculate the time from the emission to the reception of the laser pulse corresponding to the target lidar according to the relative distance information between the point cloud and the target lidar;

[0014] 2.3) Obtain the lidar beam number information of the template point cloud by looking up a table according to the vertical angle information of the template point cloud;

[0015] 2.4) Calculate the horizontal resolution of the target lidar according to the working cycle and rotation angular velocity of the lidar;

[0016] 2.5) Sort the template point cloud in ascending order of azimuth according to the horizontal angle information of the template point cloud to obtain the sorted template point cloud, and use the working cycle where the first point in the sorted template point cloud is located as the initial working cycle;

[0017] 2.6) Based on the horizontal resolution of the target lidar, calculate the working cycle numbers of each point in the sorted template point cloud according to the horizontal angle information to obtain the working cycle numbers of each point in the template point cloud and form the working cycle number information of the template point cloud;

[0018] The specific content of Step 2.6) is as follows:

[0019] 2.6.1) For each point in the sorted template point cloud, calculate the difference in the horizontal angle between the current point and the previous point according to the horizontal angle of each point in the horizontal angle information of the template point cloud;

[0020] 2.6.2) Based on the horizontal resolution of the target LiDAR, use the following formula to calculate the difference in duty cycle number between the current point and the previous point:

[0021]

[0022] in, Indicates the difference between the working cycle numbers of the i-th point and the i-1-th point in the arranged template point cloud, i∈1...N-1, N represents the total number of points in the arranged template point cloud, δ i Indicates the horizontal angle difference between the i-th point and the i-1-th point in the arranged template point cloud, Δazimuth full Indicates the horizontal resolution of the target lidar; fix() indicates the rounding operation;

[0023] 2.6.3) Calculate the working cycle number of the current point based on the difference between the working cycle numbers of the current point and the previous point, as well as the working cycle number of the previous point. The calculation formula is as follows:

[0024]

[0025] Among them, fullcycle_ID(i) and fullcycle_ID(i-1) represent the duty cycle numbers of the i-th point and the i-1-th point respectively, and laser_ID(i) and laser_ID(i-1) represent the laser radar beam numbers of the i-th point and the i-1-th point respectively;

[0026] 2.6.4) Repeat 2.6.1)-2.6.3) to process the remaining points in the arranged template point cloud, obtain the working cycle number of each point in the arranged template point cloud and form the working cycle number information of the template point cloud.

[0027] The step three is specifically as follows:

[0028] 3.1) Based on the time from the target laser radar's laser pulse from the template to the reception, the laser radar beam number information of the template point cloud, and the working cycle number information, calculate the working time of the single pulse corresponding to each point in the transmitted point cloud. The calculation formula is as follows:

[0029] Timestamp(i)=fullcycle_ID(i)*T fc +laser_ID(i)*T sfc +ToF

[0030] Among them, Timestamp(i) represents the working moment of the single pulse corresponding to the i-th point in the template point cloud, fullcycle_ID(i) represents the working cycle number of the i-th point, T fc represents the working cycle of the target lidar, laser_ID(i) represents the lidar beam number of the i-th point, T sfc represents the single-beam emission cycle of the target lidar, ToF represents the time from the emission to the reception of the laser pulse of the target lidar;

[0031] 3.2) Calculate the corresponding pulse sequence according to the working moments of each single pulse. Then, connect the four sequence points in each pulse sequence to obtain the corresponding continuous pulse signal. The pulse control signal of the target lidar is composed of the continuous pulse signals corresponding to each single pulse, which is used to control the target lidar to generate the same point cloud as the template point cloud.

[0032] The calculation formula for the pulse sequence of each single pulse in step 3.2) is as follows:

[0033] Time_ideal(i1,i2,i3,i4) = [-ε, 0, TTL, TTL + ε] + Timestamp(i)

[0034] Amp_ideal(i1,i2,i3,i4) = [0, 1, 1, 0]

[0035] Among them, Time_ideal(i1,i2,i3,i4) represents the time sequence of the pulse sequence of the i-th single pulse, Amp_ideal(i1,i2,i3,i4) represents the amplitude sequence of the pulse sequence of the i-th single pulse, i1, i2, i3, i4 are the starting point of the rising edge, the ending point of the rising edge, the starting point of the falling edge, and the ending point of the falling edge of the pulse sequence of the i-th single pulse respectively, TTL represents the pulse duration, and ε represents the time required for the rising edge of the single pulse.

[0036] The beneficial effects of the present invention are as follows:

[0037] 1. By inversely inferring the working moment of the lidar where each point is located according to the point cloud information, each point corresponds to a pulse signal, which maximally avoids the omission and distortion of the designed signal and simulates the point cloud state of the real environment as realistically as possible. The point clouds generated by the prior art are chaotic.

[0038] 2. Design the point cloud signal into a pulse sequence expanded in time, simplifying the complex three-dimensional spatial information for easy processing and analysis.

[0039] 3. The present invention provides a simple pulse sequence design method. The rising and falling processes of each single pulse are represented by four time points, and the amplitude is represented by four points corresponding to the starting point of the rising edge, the ending point of the rising edge, the starting point of the falling edge, and the ending point of the falling edge of the pulse respectively. And corresponding to the time points, it simplifies the design idea of the pulse signal and is also applicable to other pulse coding fields. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required for the description of the embodiments or the prior art. Obviously, the following drawings are only some embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other drawings can be obtained based on these drawings.

[0041] Figure 1 It is a schematic diagram of the working cycle of the lidar.

[0042] Figure 2 It is a schematic diagram from the point cloud to the TTL control signal.

[0043] Figure 3 It is the template point cloud collected in the actual situation. Figure 4 It is the flowchart of the method of the present invention. Figure 5 It is a schematic diagram of three relative positions of adjacent points in the working cycle.

[0044] Figure 6 It is a sampling schematic diagram of a single pulse.

[0045] Figure 7 It is the pulse control signal designed according to the template point cloud. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0046] Now, the exemplary embodiments of the present invention will be introduced with reference to the drawings. However, the present invention can be applied in many aspects and is not limited to the embodiments described herein. The embodiments are provided to disclose the present invention in detail and completely, and to fully convey the scope of the present invention to those skilled in the art. The terms in the exemplary embodiments shown in the drawings are not limitations on the present invention.

[0047] Unless otherwise specified, the terms (including scientific and technical terms) used herein have the ordinary meaning understood by those skilled in the relevant technical field. However, it is obvious to those skilled in the art that some alternative embodiments can be practiced using parts of the described aspects. For the purpose of explanation, specific numbers, materials, and configurations are set forth to provide a thorough understanding of the illustrative embodiments. However, it is obvious to those skilled in the art that alternative embodiments can be implemented without specific details. In other cases, some well-known features are omitted or simplified to avoid confusing the illustrative embodiments.

[0048] This embodiment takes the 16-line lidar VLP16 of Velodyne Company as an example for introduction. It should be noted that in theory, the present invention is applicable to all other mechanical rotating lidars. In lidar modeling, the target lidar is modeled with the duty cycle and operating laser parameters. Taking VLP16 as an example, the duty cycle of VLP16 is as Figure 1 shown. The time period during which all the beams of the lidar work through one round in sequence until the start of the next round is called a duty cycle (major cycle); the time period from when one beam finishes working until the next beam starts working is called a single-beam emission cycle (minor cycle). Among them, the single-beam emission cycle is divided into a reception time and a silent time, and only the light beams received during the reception time can form valid point cloud information. Currently, all rotating lidars have their fixed cycles. The design is mainly based on the laser time received by each beam.

[0049] As Figure 2 shown, the control signal design is based on the original point cloud information to design the pulse control signal. Combining the duty cycle of the lidar, each point in the point cloud corresponds one-to-one with the rising edge of the pulse control signal. The position of the time coordinate of the rising edge within the duty cycle represents the angular position where the point cloud appears, and the position within the single-beam emission cycle represents the corresponding distance.

[0050] Step 1: Collect the template point cloud of the target lidar; the schematic diagram of the collected template point cloud is as Figure 3 shown. Duty cycle (major cycle) = 55.296 μs, single-beam emission cycle (minor cycle) = 2.304 μs [[ID=

[16]

[0051] Step 2: As Figure 3 shown, perform data preprocessing on the collected template point cloud to obtain the time from the emission to the reception of the laser pulse corresponding to the target lidar, the lidar beam number information of the template point cloud, and the duty cycle number information;

[0052] The specific content of Step 2 is as follows:

[0053] 2.1) Convert the spatial position coordinate information of the acquired template point cloud into three-dimensional polar coordinate information to obtain the relative distance information between the template point cloud and the target lidar, the vertical angle information of the template point cloud, and the horizontal angle information. The relative distance information between the template point cloud and the target lidar is a set of the relative distances between each point in the template point cloud and the target lidar. The vertical angle information or horizontal angle information of the template point cloud is a set of the vertical angles or horizontal angles of each point in the template point cloud.

[0054] 2.2) Calculate the time of flight ToF from the emission to the reception of the laser pulse corresponding to the target lidar according to the relative distance R between the template point cloud and the target lidar.

[0055] The calculation formula is as follows:

[0056]

[0057] where c represents the speed of light

[0058] 2.3) Due to the one-to-one correspondence between the vertical angles of each point in the template point cloud and the lidar beam number laser_ID, the lidar beam number information of the template point cloud is obtained by looking up a table according to the vertical angle information of the template point cloud. The lidar beam number information of the template point cloud is a set of the lidar beam numbers of each point in the template point cloud. In this embodiment, the correspondence table of VLP16 is as Figure 4 shown.

[0059] Table 1 One-to-one correspondence table of laser_ID of VLP-16 and the vertical angles of each point in the emission point cloud

[0060] Angle -15° 1° -13° 3° -11° 5° -9° 7° -7° 9° -5° 11° -3° 13° -1° 15° Laser_ID 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

[0061] 2.4) Calculate the horizontal resolution Δazimuth of the target lidar according to the working period T fc and the rotational angular velocity RPM of the lidar. full where RPM (Rotation per minute) is the rotational speed of the lidar per minute. For VLP16, RPM can be set by the user between 300 and 1200, but it must be an integer multiple of 60.

[0062] The calculation formula is as follows:

[0063]

[0064] 2.5) Sort the template point cloud in ascending order of azimuth according to the horizontal angle information of the template point cloud (specifically, the horizontal angles of each point in the template point cloud) to obtain the sorted template point cloud. In specific implementation, for points with the same horizontal angle, sort them in ascending order of laser_ID, and the point cloud information that changes according to the ascending law of the horizontal azimuth can be obtained. Take the working cycle where the first point in the sorted template point cloud is located as the initial working cycle. In specific implementation, the initial working cycle is denoted as 0;

[0065] 2.6) Based on the horizontal resolution of the target lidar, calculate the working cycle number of each point in the sorted template point cloud according to the horizontal angle information, obtain the working cycle numbers of each point in the template point cloud, and form the working cycle number information of the template point cloud;

[0066] The specific steps of step 2.6) are as follows:

[0067] 2.6.1) For each point in the sorted template point cloud, calculate the difference in the horizontal angle between the current point and the previous point according to the horizontal angles of each point in the horizontal angle information of the template point cloud;

[0068] The calculation formula is as follows:

[0069] δ i =azimuth(i)-azimuth(i - 1)

[0070] 2.6.2) According to the horizontal resolution of the target lidar, use the following formula to calculate the difference in the working cycle number between the current point and the previous point:

[0071]

[0072] Where, represents the difference in the working cycle number between the i-th point and the (i - 1)-th point in the sorted template point cloud, i ∈ 1...N - 1, N represents the total number of points in the sorted template point cloud, δ i represents the difference in the horizontal angle between the i-th point and the (i - 1)-th point in the sorted template point cloud, Δazimuth full represents the horizontal resolution of the target lidar; fix() represents the rounding operation;

[0073] 2.6.3) Calculate the working cycle number of the current point according to the difference in the working cycle number between the current point and the previous point and the working cycle number of the previous point, as shown in (a)-(c) of Figure 5 : Figure 5 (a) of Figure 5 means that the two points are in the same working cycle; (b) of means that the two points are in different working cycles, and the laser_ID of the current point is greater than that of the previous point;Figure 5 In (c), the two points are in different working cycles, and the laser_ID of the current point is less than that of the previous point; the calculation formula is as follows:

[0074]

[0075] Among them, fullcycle_ID(i) and fullcycle_ID(i - 1) respectively represent the working cycle numbers of the i-th point and the (i - 1)-th point, and laser_ID(i) and laser_ID(i - 1) respectively represent the lidar beam numbers of the i-th point and the (i - 1)-th point;

[0076] 2.6.4) Repeat 2.6.1)-2.6.3) to process the remaining points in the arranged template point cloud, obtain the working cycle numbers of each point in the arranged template point cloud, and form the working cycle number information of the emitted point cloud.

[0077] Step Three: Design the pulse control signal of the target lidar according to the time from the emission to the reception of the laser pulse of the target lidar, the lidar beam number information and the working cycle number information of the template point cloud, as Figure 7 shown, for controlling the target lidar to generate the same point cloud as the template point cloud.

[0078] The specific content of Step Three is as follows:

[0079] 3.1) Calculate the working moment of each single pulse corresponding to the points in the template point cloud according to the time from the emission to the reception of the laser pulse of the target lidar, the lidar beam number information and the working cycle number information of the template point cloud. The calculation formula is as follows:

[0080] Timestamp(i) = fullcycle_ID(i) * T fc + laser_ID(i) * T sfc + ToF

[0081] Among them, Timestamp(i) represents the working moment of the i-th point corresponding to a single pulse in the template point cloud, fullcycle_ID(i) represents the working cycle number of the i-th point, T fc represents the working cycle of the target lidar, laser_ID(i) represents the lidar beam number of the i-th point, and T sfc represents the single-beam emission cycle of the target lidar, and ToF represents the time from the emission to the reception of the laser pulse of the target lidar;

[0082] 3.2) Calculate the corresponding pulse sequence according to the working moments of each single pulse. The calculation formula for the pulse sequence of each single pulse is as follows:

[0083] Time_ideal(i1,i2,i3,i4) = [-ε, 0, TTL, TTL + ε] + Timestamp(i)

[0084] Amp_ideal(i1,i2,i3,i4) = [0, 1, 1, 0]

[0085] Among them, Time_ideal(i1,i2,i3,i4) represents the time series of the pulse sequence of the i-th single pulse, Amp_ideal(i1,i2,i3,i4) represents the amplitude sequence of the pulse sequence of the i-th single pulse, i1, i2, i3, and i4 are respectively the starting point of the rising edge, the ending point of the rising edge, the starting point of the falling edge, and the ending point of the falling edge of the pulse sequence of the i-th single pulse, TTL represents the pulse duration, and ε represents the time required for the rising edge of the single pulse. In this embodiment, TTL = 10 * 10 -9 s, ε = 1 * 10 -18 .

[0086] Then, after connecting the four sequence points in each pulse sequence (i.e., the starting point of the rising edge, the ending point of the rising edge, the starting point of the falling edge, and the ending point of the falling edge of the pulse sequence), the corresponding continuous pulse signal is obtained. As shown in (a) of Figure 6 , to meet the needs of actual experiments, the pulse control signal of the target lidar is composed of the continuous pulse signals corresponding to each single pulse, as shown in Figure 7 . In specific implementation, after sampling the pulse control signal of the target lidar, the corresponding discrete pulse control signal is obtained. Because the sampling rate is often limited in actual experiments, there will be a certain error between the finally actually generated signal and the ideal signal. The discrete pulse control signal of the target lidar is input into the built hardware device, and the hardware device sends it to the target lidar to control the target lidar to generate the same point cloud as the template point cloud. The hardware device is a pulse control signal injection device mainly composed of a signal generator and a laser pulse diode.

[0087] Theoretically, after designing the lidar beam number information and the working cycle number information of the template point cloud, the present invention can generate point clouds of any shape and any distance that conform to physical laws in the lidar.

Claims

1. A method for designing a pulse control signal based on lidar target point cloud, characterized in that It includes the following steps: Step 1: The point cloud collected by the target lidar is used as the template point cloud; Step 2: Perform data preprocessing on the collected template point cloud to obtain the time from the emission to the reception of the laser pulse corresponding to the target lidar, the lidar beam number information of the template point cloud, and the working cycle number information; Step 3: Design the pulse control signal of the target lidar according to the time from the emission to the reception of the laser pulse of the target lidar, the lidar beam number information of the emitted point cloud, and the working cycle number information, so as to control the target lidar to generate the same point cloud as the template point cloud; The specific content of Step 2 is as follows: 2.1) Convert the spatial position coordinate information of the collected template point cloud into three-dimensional polar coordinate information to obtain the relative distance information between the template point cloud and the target lidar, the vertical angle information of the template point cloud, and the horizontal angle information; 2.2) Calculate the time from the emission to the reception of the laser pulse corresponding to the target lidar according to the relative distance information between the point cloud and the target lidar; 2.3) Obtain the lidar beam number information of the template point cloud by looking up a table according to the vertical angle information of the template point cloud; 2.4) Calculate the horizontal resolution of the target lidar according to the working cycle and rotational angular velocity of the lidar; 2.5) Sort the template point cloud in ascending order of azimuth angle according to the horizontal angle information of the template point cloud to obtain the sorted template point cloud, and use the working cycle where the first point in the sorted template point cloud is located as the initial working cycle; 2.6) Based on the horizontal resolution of the target lidar, calculate the working cycle numbers of each point in the sorted template point cloud according to the horizontal angle information, and obtain the working cycle number information of each point in the template point cloud and form the working cycle number information of the template point cloud.

2. A method for designing a pulse control signal based on lidar target point cloud according to claim 1, characterized in that, The specific content of Step 2.6) is as follows: 2.6.1) For each point in the sorted template point cloud, calculate the difference in the horizontal angle between the current point and the previous point according to the horizontal angles of each point in the horizontal angle information of the template point cloud; 2.6.2) According to the horizontal resolution of the target lidar, use the following formula to calculate the difference in the working cycle numbers between the current point and the previous point: Among them, represents the difference in the working cycle numbers between the i-th point and the (i - 1)-th point in the arranged template point cloud, where i ∈ 1...N - 1, N represents the total number of points in the arranged template point cloud, and δ i represents the difference in the horizontal angles between the i-th point and the (i - 1)-th point in the arranged template point cloud, and Δazimuth full represents the horizontal resolution of the target lidar; fix() represents the rounding operation; 2.6.3) Calculate the working cycle number of the current point according to the difference in the working cycle numbers between the current point and the previous point and the working cycle number of the previous point. The calculation formula is as follows: where fullcycle_ID(i) and fullcycle_ID(i - 1) respectively represent the working cycle numbers of the i-th point and the (i - 1)-th point, and laser_ID(i) and laser_ID(i - 1) respectively represent the lidar beam numbers of the i-th point and the (i - 1)-th point; 2.6.4) Repeat 2.6.1)-2.6.3) to process the remaining points in the sorted template point cloud, and obtain the working cycle numbers of each point in the sorted template point cloud and form the working cycle number information of the template point cloud.

3. A pulse control signal design method based on lidar target point cloud according to claim 1, characterized in that The specific content of Step 3 is as follows: 3.1) Calculate the working moments of each point in the emission point cloud corresponding to a single pulse according to the time from the template to the reception of the laser pulse of the target lidar, the lidar beam number information of the template point cloud, and the working cycle number information. The calculation formula is as follows: Timestamp(i) = fullcycle_ID(i) * T fc + laser_ID(i) * T sfc + ToF Among them, Timestamp(i) represents the working time of the single pulse corresponding to the i-th point in the template point cloud, fullcycle_ID(i) represents the working cycle number of the i-th point, T fc represents the working cycle of the target lidar, laser_ID(i) represents the lidar beam number of the i-th point, T sfc represents the single-beam emission cycle of the target lidar, ToF represents the time from the emission to the reception of the laser pulse of the target lidar; 3.2) Calculate the corresponding pulse sequences according to the working moments of each single pulse. Then, connect the four sequence points in each pulse sequence to obtain the corresponding continuous pulse signal. The pulse control signal of the target lidar is composed of the continuous pulse signals corresponding to each single pulse, and is used to control the target lidar to generate the same point cloud as the template point cloud.

4. A method for designing a pulse control signal based on lidar target point cloud according to claim 3, characterized in that, The calculation formula of the pulse sequence of each single pulse in step 3.2) is as follows: Time_ideal(i1,i2,i3,i4)=[-ε,0,TTL,TTL+ε]+Timestamp(i) Amp_ideal(i1,i2,i3,i4)=[0,1,1,0] Where, Time_ideal(i1,i2,i3,i4) represents the time sequence of the pulse sequence of the i-th single pulse, Amp_ideal(i1,i2,i3,i4) represents the amplitude sequence of the pulse sequence of the i-th single pulse, i1, i2, i3, i4 are the start point of the rising edge, the end point of the rising edge, the start point of the falling edge, and the end point of the falling edge of the pulse sequence of the i-th single pulse respectively, TTL represents the pulse duration, and ε represents the time required for the rising edge of a single pulse.

Images