Gear ring water immersion ultrasonic defect detection device and detection method

Abstract

A water immersion ultrasonic defect detection device and method for gear rings is disclosed, relating to a water immersion ultrasonic testing technology. This invention addresses the problem that current ultrasonic testing of gear rings relies heavily on manual labor, leading to large errors and low efficiency. The invention uses a liftable rotary table positioned within a water tank to hold the gear ring; a single-axis lifting device is fixed to the tank, and a water immersion ultrasonic probe is mounted on the lifting device; an inlet pipe leads into the tank from its side wall, and an outlet pipe leads out from its bottom; the rotation direction, speed, and height of the rotary table are controlled by a rotation control signal from an industrial control computer; the industrial control computer is connected to a computer and an ultrasonic signal generator; the ultrasonic signal generator is connected to the water immersion ultrasonic probe; and the water immersion ultrasonic probe is connected to the industrial control computer; the computer generates a defect image based on the echo signal. The beneficial effect is improved defect detection efficiency.

Description

Technical Field

[0001] This invention relates to a water immersion ultrasonic testing technique. Background Technology

[0002] Gear rings are internal gears formed by machining teeth on the inner surface. They are a type of engineering component widely used in modern industries, ranging from small fixed gears inside vacuum cleaners to high-speed gear transmission systems in aircraft engines. The applications of gears are extremely wide, and our requirements for gear precision are becoming increasingly stringent. Therefore, it is particularly important to establish a complete detection system for internal defects of gear rings.

[0003] The main processing steps involved in the production and use of gear rings include: raw material cutting, heating, forging, punching, ring rolling, tempering, rough turning, quenching and tempering, finish turning, gear shaping, and nitriding. Internal defects that can easily occur during these steps include holes, cracks, inclusions of nitrided structures, network cracks, and intergranular oxidation. Quality inspection of gear rings is an essential step. Commonly used inspection methods in industrial production include metallographic inspection, low-magnification inspection, ultrasonic testing, radiographic testing, and eddy current testing. Metallographic and low-magnification inspections are destructive tests, often used for the physicochemical analysis of gear rings. Radiographic testing produces radiation signals that can affect human health. Eddy current testing has limitations, only applicable to conductive workpieces. Ultrasonic testing is a commonly used method for detecting internal defects in forgings. It uses an ultrasonic transducer to emit and receive ultrasonic waves, and the waveform signal is used to determine the presence and equivalent size of internal defects in the gear ring. However, ultrasonic testing still relies heavily on manual labor, has low automation, and results in large errors and low efficiency in defect detection. Summary of the Invention

[0004] The purpose of this invention is to solve the problems of large errors and low efficiency in the existing ultrasonic testing of gear rings, which relies heavily on manual labor. This invention proposes a water immersion ultrasonic defect testing device and method for gear rings.

[0005] The present invention discloses a water immersion ultrasonic defect detection device for gear rings. The detection device includes a water tank, a liftable rotary table, a single-axis lifting device, a water inlet pipe, a water outlet pipe, a water immersion ultrasonic probe, an industrial control computer, and an ultrasonic signal generator.

[0006] The liftable rotary table is located at the center of the bottom surface of the water tank; the liftable rotary table is used to fix the gear ring to be tested.

[0007] The single-axis lifting device is fixed on the water tank;

[0008] The water immersion ultrasonic probe is mounted on a single-axis lifting device to adjust the height of the water immersion ultrasonic probe (7) on the outer side of the gear ring (11) to be tested. The ultrasonic waves emitted by the water immersion ultrasonic probe are perpendicularly incident from the outer surface along the radial direction of the gear ring.

[0009] The inlet pipe is introduced through the side wall of the pool, and the outlet pipe is led out from the bottom of the pool.

[0010] The rotation direction, rotation speed, and height of the liftable rotary table are controlled by rotation control signals sent by the industrial control computer.

[0011] The command signal input terminal of the industrial control computer is connected to the command signal output terminal of the computer; the acoustic control signal output terminal of the industrial control computer is connected to the acoustic control signal input terminal of the ultrasonic signal generator; the ultrasonic signal output terminal of the ultrasonic signal generator is connected to the ultrasonic signal input terminal of the water immersion ultrasonic probe; the acquisition signal output terminal of the water immersion ultrasonic probe is connected to the acquisition signal input terminal of the industrial control computer; the echo signal output terminal of the industrial control computer is connected to the echo signal input terminal of the computer; the computer generates a defect image based on the received echo signal.

[0012] Furthermore, the testing device also includes a flange;

[0013] The water immersion ultrasonic probe is mounted on a single-axis lifting device via a flange.

[0014] Furthermore, the single-axis lifting device includes a base, a column, and a landing gear;

[0015] The base is fixed to the top of the side wall of the pool, and the column is vertically fixed to the side wall of the base, with the column located directly above the pool; the landing gear is set on the side wall of the column, and the landing gear slides up and down along the column.

[0016] The flange is fixed to the bottom end of the landing gear;

[0017] The water immersion ultrasonic probe is fixed to the side wall of the flange.

[0018] A method for ultrasonic defect detection of gear rings by water immersion, the method comprising the following steps:

[0019] Step 1: Perform a coarse scan on the gear ring to be inspected to obtain the preliminary area of ​​the defect;

[0020] Step 2: Perform a fine scan on the preliminary defect area obtained in Step 1 to obtain a refined image of the internal defect of the gear ring;

[0021] The specific process of fine scanning in step two is as follows:

[0022] Step 2: Divide the initial defect area into n emission points at equal intervals. The locations of the n emission points are denoted as emission point S1, emission point S2, emission point S3, emission point S4, ..., emission point Sn.

[0023] Step 22: Adjust the height-adjustable rotary table, align the immersion ultrasonic probe with the S1 emission point, excite the immersion ultrasonic probe 7 to collect a set of echo signals, and simulate the echo signals of S2, S3, S4, ..., Sn according to the distribution of the sound field.

[0024] Steps 2 and 3: Adjust the height-adjustable rotary table again, align the immersion ultrasonic probe with the S2 emission point, excite the immersion ultrasonic probe to collect another set of echo signals, and simulate the echo signals of S1, S3, S4, ..., Sn according to the distribution of the sound field; and so on, to obtain the n*n echo full matrix data.

[0025] Step 24: Establish an xz coordinate system in the imaging area, with the x-direction representing the circumferential direction of the gear and the z-direction representing the radial direction of the gear;

[0026] Step 25: Divide the imaging area into m×n cells, each cell being considered a virtual focal point, denoted as P(x, z); where m is a positive integer;

[0027] Step 26: Using virtual focusing, focus each group of time-domain signals in the n*n echo full matrix data obtained in Step 23 onto the focusing point in Step 25, and complete the focusing calculation for all the focusing points to obtain the refined image of the internal defects of the gear ring.

[0028] Furthermore, the specific process of coarse scanning in step one is as follows:

[0029] First, keep the height of the adjustable rotary table constant and only adjust the rotation angle of the adjustable rotary table. The size of the rotation angle should be such that the corresponding arc length is twice the incident area of ​​the immersion ultrasonic probe. This enables the immersion ultrasonic probe to perform a circumferential scan of the gear ring to be tested at a certain height. The industrial control computer transmits the echo signal to the computer, and the computer completes the B-type scanning imaging of the gear ring at that height.

[0030] Secondly, the height of the adjustable rotary table is adjusted so that the water immersion ultrasonic probe can complete the above-mentioned multi-layer circumferential scanning on the surface of the gear ring to be tested. The height interval of each layer is two body positions of the incident area of ​​the water immersion ultrasonic probe, and the cross-section of each layer is completed by computer B-mode scanning imaging.

[0031] Finally, by combining multi-layer B-mode scanning imaging, a radial full-circumference C-mode three-dimensional imaging of the gear ring was completed, and the location information of the defect inside the gear ring was determined.

[0032] Furthermore, the specific formula for the focused calculation in step two six is ​​as follows:

[0033]

[0034] Where I(x,z) is the imaging intensity at the focal point P(x,z); t is the propagation time from when the probe emits at position i, passes through a focal point P(x,z) in the imaging region, and is received at position j; h ij [·] represents the time-domain expression of the signal, and n is the total number of transmission points.

[0035] The beneficial effects of this invention are as follows: Using water immersion ultrasonic testing to detect internal defects in gear rings is superior to destructive methods such as metallography and low-magnification methods, as ultrasonic testing does not damage the performance of the gear rings. Compared to non-destructive methods such as X-ray testing, ultrasonic testing does not generate radiation signals that affect the human body, making it more suitable for forging inspection. Furthermore, it overcomes the limitation of eddy current testing, which is only applicable to conductive workpieces, and is extremely effective in measuring internal defects in gear rings. The detection device provided by this invention achieves automated detection of gear ring defects, reducing reliance on manual labor, improving defect detection efficiency and accuracy, and reducing labor costs while increasing economic benefits. The detection method of this invention incorporates virtual array elements, achieving phased array full-focus imaging with a single virtual array element probe. Through a one-to-many transmission and multiple-receiver approach, more detailed scanning is achieved at the defect location, refining the approximate location and contour information of the defect. This C-type scanning method, combining coarse and fine scanning, eliminates a large number of unnecessary ultrasonic testing areas, saving energy and improving defect detection efficiency. Attached Figure Description

[0036] Figure 1 This is a three-dimensional structural diagram of a gear ring water immersion ultrasonic defect detection device as described in Specific Embodiment 1;

[0037] Figure 2 This is a schematic diagram showing the positional relationship between the water immersion ultrasonic probe and the gear ring to be tested in Specific Implementation Method 1.

[0038] Figure 3 This is a schematic diagram of a gear ring water immersion ultrasonic defect detection device as described in Specific Implementation Method 1;

[0039] Figure 4 This is a flowchart illustrating the detailed scanning process in Implementation Method Two. Detailed Implementation

[0040] Specific Implementation Method 1: Combination Figures 1 to 3This embodiment describes a gear ring water immersion ultrasonic defect detection device, which includes a water tank 1, a liftable rotary table 2, a single-axis lifting device 3, a water inlet pipe 5, a water outlet pipe 6, a water immersion ultrasonic probe 7, an industrial control computer 8, and an ultrasonic signal generator 10.

[0041] The liftable rotary table 2 is located at the center of the bottom surface inside the water tank 1; the liftable rotary table 2 is used to fix the gear ring 11 to be tested;

[0042] The single-axis lifting device 3 is fixed on the water tank 1;

[0043] The water immersion ultrasonic probe 7 is mounted on the single-axis lifting device 3; the single-axis lifting device 3 drives the water immersion ultrasonic probe 7 to move up and down on the outer side of the gear ring 11 to be tested, so that the ultrasonic waves emitted by the water immersion ultrasonic probe 7 are perpendicularly incident from the outer surface along the radial direction of the gear ring 11; the single-axis lifting device 3 is used to fix the water immersion ultrasonic probe 7 at the bottom of the water tank 1, so that the water immersion ultrasonic probe 7 is aligned with the gear ring 11.

[0044] The inlet pipe 5 is introduced through the side wall of the water tank 1, and the outlet pipe 6 is led out from the bottom of the water tank 1. Water is injected into the water tank 1 through the inlet pipe 5 and drained out of the water tank 1 through the outlet pipe 6. Water valves are provided at the ends of the inlet pipe 5 and the outlet pipe 6 respectively. When the outlet pipe 6 is closed, water is injected into the water tank 1 by opening the inlet pipe 5. The water level in the water tank 1 is controlled by controlling the water injection time. After the test is completed, the water in the water tank 1 is drained by opening the outlet pipe 6, so that the liftable rotary table 2 is removed from the water environment, thereby increasing the service life of the liftable rotary table 2.

[0045] The rotation direction, rotation speed, and height of the liftable rotary table 2 are controlled by rotation control signals sent by the industrial control computer 8.

[0046] The instruction signal input terminal of the industrial control computer 8 is connected to the instruction signal output terminal of the computer 9. The acoustic control signal output terminal of the industrial control computer 8 is connected to the acoustic control signal input terminal of the ultrasonic signal generator 10. The ultrasonic signal output terminal of the ultrasonic signal generator 10 is connected to the ultrasonic signal input terminal of the water immersion ultrasonic probe 7. The acquisition signal output terminal of the water immersion ultrasonic probe 7 is connected to the acquisition signal input terminal of the industrial control computer 8. The echo signal output terminal of the industrial control computer 8 is connected to the echo signal input terminal of the computer 9. The computer 9 generates a defect image based on the received echo signal.

[0047] In this embodiment, the water immersion ultrasonic probe 7 is fixed in the water tank 1, and the ultrasonic waves emitted by the water immersion ultrasonic probe 7 are incident perpendicularly from the outer surface along the radial direction of the gear ring 11. The rotation angle and lifting height of the liftable rotary table 2 are controlled by the rotation control signal issued by the industrial control computer 8 to achieve full circumference scanning of the gear ring 11. The rotation angle and lifting height of the liftable rotary table 2 are controlled by the rotation control signal issued by the industrial control computer 8. The industrial control computer 8 is connected to the computer 9, and the computer 9 issues a command signal to control the industrial control computer 8 to generate a sound wave control signal. The sound wave control signal is output to the ultrasonic signal generator 10, and the ultrasonic signal generator 10 generates an ultrasonic wave signal which is transmitted to the water immersion ultrasonic probe 7. The water immersion ultrasonic probe 7 emits ultrasonic waves that are incident perpendicularly from the outer surface along the radial direction of the gear ring 11. The water immersion ultrasonic probe 7 also acts as a receiver to transmit the echo signal to the acquisition card of the industrial control computer 8. The industrial control computer 8 transmits the echo signal to the computer 9 in real time to complete the imaging of internal defects in the gear ring 11.

[0048] In a preferred embodiment, the detection device further includes a flange 4;

[0049] The water immersion ultrasonic probe 7 is mounted on the single-axis lifting device 3 via flange 4.

[0050] In this embodiment, the flange 4 serves as a connector and makes it easier to fix the immersion ultrasonic probe 7. The immersion ultrasonic probe 7 is fixed on the single-axis lifting device 3 using the flange 4 and kept stationary after adjusting to a suitable height.

[0051] In a preferred embodiment, the single-axis lifting device 3 includes a base 3-1, a column 3-2, and a landing gear 3-3;

[0052] The base 3-1 is fixed to the top of the side wall of the pool 1, and the column 3-2 is vertically fixed to the side wall of the base 3-1, with the column 3-2 located directly above the pool 1; the landing gear 3-3 is set on the side wall of the column 3-2, and the landing gear 3-3 slides up and down along the column 3-2.

[0053] The flange 4 is fixed to the bottom end of the landing gear 3-3;

[0054] The water immersion ultrasonic probe 7 is fixed on the side wall of the flange 4.

[0055] In this embodiment, the single-axis lifting device 3 is used to fix the water immersion ultrasonic probe 7 inside the water tank 1.

[0056] Specific Implementation Method Two: Combination Figure 4 This embodiment describes a method for detecting defects in gear rings using ultrasonic immersion testing. The method includes the following steps:

[0057] Step 1: Perform a coarse scan on the gear ring 11 to be inspected to obtain the preliminary area of ​​the defect;

[0058] Step 2: Perform a fine scan on the preliminary defect area obtained in Step 1 to obtain a refined image of the internal defect of the gear ring;

[0059] The specific process of fine scanning in step two is as follows:

[0060] Step 2: Divide the initial defect area into n emission points at equal intervals. The locations of the n emission points are denoted as emission point S1, emission point S2, emission point S3, emission point S4, ..., emission point Sn.

[0061] Step 2: Adjust the liftable rotary table 2, align the water immersion ultrasonic probe 7 with the S1 emission point, excite the water immersion ultrasonic probe 7 to collect a set of echo signals, and simulate the echo signals of S2, S3, S4, ..., Sn according to the distribution of the sound field.

[0062] Steps 2 and 3: Adjust the height-adjustable rotary table 2 again, align the water immersion ultrasonic probe 7 with the S2 emission point, excite the water immersion ultrasonic probe 7 to collect another set of echo signals, and simulate the echo signals of S1, S3, S4, ..., Sn according to the distribution of the sound field; and so on, to obtain the n*n echo full matrix data.

[0063] Step 24: Establish an xz coordinate system in the imaging area, with the x-direction representing the circumferential direction of the gear and the z-direction representing the radial direction of the gear;

[0064] Step 25: Divide the imaging area into m×n cells, each cell being considered a virtual focal point, denoted as P(x, z); where m is a positive integer;

[0065] Step 26: Using virtual focusing, focus each group of time-domain signals in the n*n echo full matrix data obtained in Step 23 onto the focusing point in Step 25, and complete the focusing calculation for all the focusing points to obtain the refined image of the internal defects of the gear ring.

[0066] In the preferred embodiment, the specific process of coarse scanning in step one is as follows:

[0067] First, keep the height of the adjustable rotary table 2 constant, and only adjust the rotation angle of the adjustable rotary table 2. The size of the rotation angle should be such that the corresponding arc length is twice the incident area of ​​the water immersion ultrasonic probe 7, so as to realize the circumferential scanning of the gear ring 11 to be tested by the water immersion ultrasonic probe 7 at a certain height. The industrial control computer 8 transmits the echo signal to the computer 9, and the computer 9 completes the B-type scanning imaging of the gear ring on the cross section at that height.

[0068] Secondly, the height of the adjustable rotating stage 2 is adjusted so that the water immersion ultrasonic probe 7 completes the above-mentioned multi-layer circumferential scanning on the surface of the gear ring 11 to be tested. The height interval of each layer is two body positions of the incident area of ​​the water immersion ultrasonic probe 7, and the cross section of each layer is B-type scanning imaging completed by the computer 9.

[0069] Finally, by combining multi-layer B-mode scanning imaging, a radial full-circumference C-mode scanning three-dimensional imaging of the gear ring 11 was completed, and the location information of the defect inside the gear ring 11 was determined.

[0070] In this embodiment, the water immersion ultrasonic probe 7 is fixed inside the water tank 1, and the gear ring 11 is placed on the liftable rotary table 2. The circumferential scanning of the water immersion ultrasonic probe 7 is achieved by adjusting the orientation of the gear ring 11 using the liftable rotary table 2. During the coarse scan, the interval between each ultrasonic wave emission position of the water immersion ultrasonic probe 7 is based on twice the ultrasonic incident area. The rotation angle and lifting height of the liftable rotary table 2 are controlled by the industrial control computer 8 to achieve all-round scanning of the water immersion ultrasonic probe 7. The echo signal received by the water immersion ultrasonic probe 7 is transmitted to the signal acquisition card of the industrial control computer 8 and then transmitted to the computer 9 in real time, which can realize the imaging of internal defects of the gear ring 11.

[0071] In the preferred embodiment, the specific formula for the focusing calculation in step two-six is ​​as follows:

[0072]

[0073] Where I(x,z) is the imaging intensity at the focal point P(x,z); t is the propagation time from when the probe emits at position i, passes through a focal point P(x,z) in the imaging region, and is received at position j; h ij [·] represents the time-domain expression of the signal, and n is the total number of transmission points.

[0074] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A gear ring water immersion ultrasonic defect detection method, which is realized based on a gear ring water immersion ultrasonic defect detection device, the detection device comprising a water tank (1), a liftable rotary table (2), a single-shaft lifting device (3), a water inlet pipe (5), a water outlet pipe (6), a water immersion ultrasonic probe (7), an industrial computer (8) and an ultrasonic signal generator (10); the liftable rotary table (2) is arranged at the center of the bottom surface of the water tank (1); the liftable rotary table (2) is used for fixing the gear ring (11) to be detected; the single-shaft lifting device (3) is fixed on the water tank (1); the water immersion ultrasonic probe (7) is installed on the single-shaft lifting device (3); the water immersion ultrasonic probe (7) is used for adjusting the height position of the water immersion ultrasonic probe (7) on the outer side surface of the gear ring (11) to be detected, and the ultrasonic waves emitted by the water immersion ultrasonic probe (7) are vertically incident along the radial direction of the gear ring (11); the water inlet pipe (5) is introduced from the side wall of the water tank (1), and the water outlet pipe (6) is led out from the bottom surface of the water tank (1); the rotation direction and speed of the liftable rotary table (2) and the height of the table surface of the liftable rotary table (2) are controlled by the rotation control signal emitted by the industrial computer (8); the instruction signal input end of the industrial computer (8) is connected with the instruction signal output end of a computer (9), the acoustic wave control signal output end of the industrial computer (8) is connected with the acoustic wave control signal input end of the ultrasonic signal generator (10), the ultrasonic signal output end of the ultrasonic signal generator (10) is connected with the ultrasonic signal input end of the water immersion ultrasonic probe (7), the collection signal output end of the water immersion ultrasonic probe (7) is connected with the collection signal input end of the industrial computer (8), the echo signal output end of the industrial computer (8) is connected with the echo signal input end of the computer (9), and the computer (9) generates a defect image according to the received echo signal; characterized in that the detection method comprises the following steps: Step one, rough scanning of the gear ring (11) to be detected to obtain a preliminary region of defects; Step two, fine scanning of the preliminary region of defects obtained in step one to obtain a refined internal defect image of the gear ring; the specific process of the fine scanning in step two is as follows: Step two one, equally dividing the preliminary region of defects into n emission points, and the positions of the n emission points are respectively denoted as emission point S1, emission point S2, emission point S3, emission point S4, …, and emission point Sn; Step two two, adjusting the liftable rotary table (2) to align the water immersion ultrasonic probe (7) with the S1 emission point, exciting the water immersion ultrasonic probe (7) to collect a group of echo signals, and simulating the echo signals of S2, S3, S4, …, and Sn according to the distribution of the acoustic field; Step two three, adjusting the liftable rotary table (2) again to align the water immersion ultrasonic probe (7) with the S2 emission point, exciting the water immersion ultrasonic probe (7) to collect a group of echo signals again, and simulating the echo signals of S1, S3, S4, …, and Sn according to the distribution of the acoustic field; and the like, to obtain an n*n echo matrix data. Step two four, an x-z coordinate system is established in the imaging area, the x direction is the gear circumferential direction, and the z direction is the gear radial direction; Step two five, the imaging area is divided into m*n unit cells, each unit cell is regarded as a virtual focal point, and the virtual focal point is P(x, z); wherein m is a positive integer; Step two six, each group of time domain signals in the n*n echo full matrix data obtained in step two three is focused on the focal point in step two five through the virtual focusing mode, and the focusing calculation is completed for all the focal points, that is, the refined gear ring internal defect image is obtained.

2. The method according to claim 1, wherein, The detection device also comprises a flange (4); The water immersion ultrasonic probe (7) is installed on the single-axis lifting device (3) through the flange (4).

3. The method of claim 2, wherein the gear sleeve is immersed in water. The single-axis lifting device (3) comprises a base (3-1), a column (3-2) and a landing gear (3-3); The base (3-1) is fixed to the top of the side wall of the water tank (1), the column (3-2) is vertically fixed to the side wall of the base (3-1), and the column (3-2) is located directly above the water tank (1); the landing gear (3-3) is arranged on the side wall of the column (3-2), and the landing gear (3-3) slides up and down along the column (3-2); The flange (4) is fixed to the bottom end of the landing gear (3-3); The water immersion ultrasonic probe (7) is fixed to the side wall of the flange (4).

4. The method of claim 1, wherein, The specific process of the rough scanning in step one is as follows: Firstly, the height of the liftable rotary table (2) is unchanged, only the rotation angle of the liftable rotary table (2) is adjusted, the size of the rotation angle should be such that the corresponding arc length is twice the incident area of the water immersion ultrasonic probe (7), so as to realize the circumferential scanning of the water immersion ultrasonic probe (7) on the gear ring (11) to be detected at a certain height, and the echo signal is transmitted into the computer (9) by the industrial computer (8), and the gear B-mode scanning imaging on the section is completed by the computer (9); Secondly, the height of the liftable rotary table (2) is adjusted, so that the water immersion ultrasonic probe (7) completes the multi-layer detection of the above circumferential scanning on the surface of the gear ring (11) to be detected, and the height interval of each layer is twice the size of the incident area of the water immersion ultrasonic probe (7), and the B-mode scanning imaging of each layer section is completed by the computer (9); Finally, the radial full-circle C-mode scanning three-dimensional imaging of the gear ring (11) is completed by combining the multi-layer B-mode scanning imaging, and the position information of the defect in the gear ring (11) is determined.

5. The method of claim 1, wherein, The specific formula of the focusing calculation in step two six is as follows: wherein is the imaging intensity of the focus point P(x, z); t is the propagation time of a signal emitted by the probe at position i through a certain focus point P(x, z) of the imaging region, received at position is the time-domain representation of this signal, n is the total number of emission points.

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