Frequency modulated continuous wave laser radar phase noise compensation method and device

Abstract

The invention discloses a frequency modulated continuous wave laser radar phase noise compensation method. The frequency modulation continuous optical signal is divided into two paths: a measurement path and an auxiliary path; the frequency modulation continuous optical signal of the measurement path is divided into two paths, one path is used as a reference optical signal, the other path is used as a detection optical signal to be emitted to a target, and beat frequency is carried out on the received target reflection optical signal and the reference optical signal to obtain a beat frequency signal of the measurement path; the frequency modulation continuous optical signal of the auxiliary path passes through a Mach-Zehnder interferometer with a fixed time delay difference and then is subjected to beat frequency to obtain an auxiliary path beat frequency signal; searching and determining the frequency of the beat frequency signal of the measurement path, and extracting the phase noise in the beat frequency signal of the auxiliary path; estimating the phase noise of the measurement path; and finally compensating the phase noise. The invention also discloses a frequency modulated continuous wave laser radar phase noise compensation device. Compared with the prior art, the calculation amount of digital processing can be greatly reduced.

Description

Technical Field

[0001] The present invention relates to a laser radar phase noise compensation method, and in particular to a frequency modulated continuous wave (FMCW) laser radar phase noise compensation method and device, belonging to the laser radar technical field. Background Art

[0002] Frequency modulated continuous wave (FMCW) lidar is an emerging ranging and imaging technology that is widely used in autonomous driving, drones, environmental monitoring and other fields. Its basic principle is to perceive target information by emitting a linear frequency modulated laser signal, receiving the signal reflected from the target, and comparing the frequency difference between the two. According to the Doppler effect, the speed of the target object can be obtained by analyzing the frequency shift in the echo signal. This process enables FMCW lidar to achieve high-precision and real-time ranging and speed measurement. Compared with traditional pulse lidar, FMCW lidar has several significant advantages. First, FMCW radar can provide higher resolution because it uses a continuous waveform instead of discrete pulses, which can obtain more data points in a short time, thereby improving imaging quality and detail performance. Second, due to the continuous emission and reception of signals, FMCW radar can still effectively detect distant targets under low energy conditions, making it perform better in complex environments. In addition, FMCW radar is more sensitive to small objects and low-reflectivity surfaces, which helps to improve detection capabilities in various application scenarios.

[0003] FMCW lidar can achieve signal modulation in two main ways: external modulation and internal modulation. External modulation is to frequency modulate the emitted laser signal through additional equipment after the laser is emitted. This process increases the size and cost of the system, and may also introduce additional noise and delay. Internal modulation refers to the frequency change of the emitted laser beam directly inside the laser, which is usually achieved by changing the driving current or temperature of the laser. In contrast, internal modulation has several significant advantages. First, since all operations are completed inside the laser, the connection between components is reduced, which helps to improve system stability and reliability. Secondly, internal modulation usually has a higher frequency response speed, which makes the signal adjustment faster, thereby improving the ranging accuracy.

[0004] However, the performance of the FMCW lidar system based on internal modulation is limited by multiple influencing factors, such as frequency sweep nonlinearity, phase noise, etc. Among them, the frequency sweep nonlinearity can be calibrated by the preprocessed modulated current signal. Then, the phase noise mainly comes from the spontaneous radiation of the laser and the changes in the external environment. Since the FMCW lidar calculates the target distance by comparing the frequency difference between the transmitted and received signals, this noise will cause the frequency offset between the transmitted signal and the received signal, which directly affects the accuracy of the ranging and speed measurement. At the same time, the impact of phase noise will increase with the increase of the measured distance. When detecting moving objects, the speed information is obtained by analyzing the frequency offset of the echo signal. If there is a large phase noise, this frequency offset will be masked, resulting in significant errors in the speed estimation.

[0005] Therefore, it is necessary to eliminate or compensate for the phase noise, so as to improve the measurement distance and accuracy of the FMCW laser radar system. Reference [1] proposed a phase noise compensation method based on digital processing. This method divides the frequency modulated continuous optical signal into two paths: the measurement path and the auxiliary path; the frequency modulated continuous optical signal of the measurement path is divided into two paths, one path is used as the reference optical signal, and the other path is used as the detection optical signal to be transmitted to the target, and the received target reflected optical signal is beat with the reference optical signal to obtain the measurement path beat signal; the optical signal of the auxiliary path is passed through an electro-optical modulator with a fixed frequency shift and then beat with the auxiliary path beat signal to obtain the auxiliary path beat signal; finally, the measurement path phase noise is compensated by digitally processing the auxiliary path beat signal and the measurement path beat signal. This scheme improves the compensation accuracy of phase noise, reduces the requirements for laser line width and auxiliary hardware, and further improves the dynamic range of distance measurement. However, this scheme does not accurately estimate the phase noise of the measurement path, but rather selects the optimal solution based on the results of different phase noise compensation by traversing the delay parameters of the phase noise within a certain range, and the document does not explain how to determine the above delay range. In addition, in order to obtain better results, the range needs to be continuously refined, which significantly increases the computational burden of data processing.

[0006] References:

[0007] [1]Xu C, et al.Adaptive carrier-phase-noise-canceled LiDAR for range-Doppler imaging beyond hundreds of laser coherence length[J].Optics Letters, 2024,49(15):4150-4153. Summary of the invention

[0008] The technical problem to be solved by the present invention is to overcome the shortcomings of the prior art and provide a frequency modulated continuous wave laser radar phase noise compensation method, which can accurately estimate the phase noise of the measurement path and perform phase noise compensation accordingly without traversing all possibilities to determine the optimal solution, and can be implemented automatically to avoid the need for manual intervention.

[0009] The present invention specifically adopts the following technical solutions to solve the above technical problems:

[0010] A frequency modulated continuous wave laser radar phase noise compensation method, the frequency modulated continuous wave laser radar divides the frequency modulated continuous light signal into two paths: a measurement path and an auxiliary path; the frequency modulated continuous light signal of the measurement path is divided into two paths, one path is used as a reference light signal, and the other path is used as a detection light signal to be emitted to the target, and the received target reflected light signal is beat with the reference light signal to obtain the measurement path beat signal; the frequency modulated continuous light signal of the auxiliary path passes through a fixed delay difference τ r The auxiliary path beat signal is obtained by performing the following digital processing on the auxiliary path beat signal and the measurement path beat signal to obtain the phase noise of the measurement path, and then the obtained measurement path phase noise is compensated:

[0011] First, the frequency range of the measurement path beat frequency signal is preliminarily searched out, and then the linear frequency modulation z-transform method is used to determine the frequency of the measurement path beat frequency signal within the preliminarily searched frequency range. At the same time, the phase noise in the auxiliary path beat signal is extracted The phase noise of the measurement path is estimated according to the following formula:

[0012]

[0013] in, round[·] means rounding to the nearest integer, γτ r is the beat frequency of the auxiliary path beat signal,

[0014] Preferably, the frequency range of the beat frequency signal of the measurement path is preliminarily searched out using the improved binary search method, specifically as follows: the entire frequency band interval is divided into three parts, and there is overlap between every two adjacent parts of the three parts; the average power of the three parts is calculated and the part with the largest average power is selected to repeat the above process; iterate in sequence until the width of the final selected partial frequency band meets the preset requirements.

[0015] Preferably, the following method is used to compensate the obtained phase noise of the measurement path: according to the estimated phase noise of the measurement path Constructing compensation factors Then use the compensation factor Multiplied by the measurement path beat frequency signal.

[0016] Based on the same inventive concept, the following technical solutions can also be obtained:

[0017] A frequency modulated continuous wave laser radar phase noise compensation device, the frequency modulated continuous wave laser radar divides the frequency modulated continuous light signal into two paths: a measurement path and an auxiliary path; the frequency modulated continuous light signal of the measurement path is divided into two paths, one path is used as a reference light signal, and the other path is used as a detection light signal to be emitted to the target, and the received target reflected light signal is beat with the reference light signal to obtain the measurement path beat signal; the frequency modulated continuous light signal of the auxiliary path passes through a fixed delay difference τ r The Mach-Zehnder interferometer is then used to perform a beat frequency to obtain an auxiliary path beat frequency signal; the frequency modulated continuous wave laser radar phase noise compensation device obtains the phase noise of the measurement path by performing the following digital processing on the auxiliary path beat frequency signal and the measurement path beat frequency signal, and then compensates for the obtained measurement path phase noise, specifically including:

[0018] A frequency range search module is used to preliminarily search for the frequency range of the beat frequency signal of the measurement path;

[0019] Frequency estimation module, used to determine the frequency of the beat signal of the measurement path within the frequency range preliminarily searched using the linear frequency modulation z-transform method

[0020] Phase noise extraction module, used to extract the phase noise in the auxiliary path beat frequency signal The measurement path phase noise estimation module is used to estimate the phase noise of the measurement path according to the following formula

[0021]

[0022] in, round[·] means rounding to the nearest integer, γτ r is the beat frequency of the auxiliary path beat signal,

[0023] The phase noise compensation module is used to compensate the phase noise of the obtained measurement path.

[0024] Preferably, the frequency range search module uses a modified binary search method to preliminarily search for the frequency range of the beat frequency signal of the measurement path, specifically as follows: the entire frequency band interval is divided into three parts, and there is overlap between every two adjacent parts of the three parts; the average power of the three parts is calculated and the part with the largest average power is selected to repeat the above process; iterate in sequence until the width of the final selected partial frequency band meets the preset requirements.

[0025] Preferably, the phase noise compensation module uses the following method to compensate the obtained phase noise of the measurement path: according to the estimated phase noise of the measurement path Constructing compensation factors Then use the compensation factor Multiplied by the measurement path beat frequency signal.

[0026] Compared with the prior art, the technical solution of the present invention has the following beneficial effects:

[0027] The present invention is based on digital processing technology and can accurately estimate the phase noise of the measurement path, and then effectively eliminate the adverse effects of phase noise on distance and speed measurement results through phase noise compensation, thereby improving detection accuracy; the digital processing process of the present invention is simple, reduces the amount of calculation, can effectively improve the real-time performance of radar detection, and reduce the requirements for hardware performance. BRIEF DESCRIPTION OF THE DRAWINGS

[0028] Figure 1 This is a schematic diagram of the structural principle of the frequency modulated continuous wave laser radar phase noise compensation device of the present invention;

[0029] Figure 2 This is the principle diagram of frequency modulated continuous wave laser radar distance measurement and speed measurement;

[0030] Figure 3 This is the result diagram of searching the frequency range of the beat frequency signal of the measurement path;

[0031] Figure 4 This is the result diagram of the CZT frequency estimation of the measurement path beat signal;

[0032] Figure 5 This is the result diagram after the phase noise compensation processing of the beat frequency signal of the measurement path;

[0033] Figure 6 is the peak value of the signal power spectrum density after phase noise compensation for different N and p. DETAILED DESCRIPTION

[0034] In view of the shortcomings of the prior art, the solution of the present invention is to improve the digital processing part thereof, estimate the phase noise of the measurement path by digitally processing the auxiliary path beat frequency signal and the measurement path beat frequency signal, and then compensate for the obtained phase noise of the measurement path.

[0035] To facilitate public understanding, the technical solution of the present invention is described in detail below with reference to the accompanying drawings:

[0036] The basic structure of the frequency modulated continuous wave laser radar phase noise compensation device of the present invention is as follows: Figure 1 As shown, an arbitrary waveform generator generates a modulation signal to control the adjustable laser light, and generates a linear frequency modulated continuous optical signal whose frequency changes with an applied voltage; the generated frequency modulated continuous optical signal is divided into two paths: a measurement path and an auxiliary path; the frequency modulated continuous optical signal of the measurement path is divided into two paths, one path is used as a reference optical signal, and the other path is used as a detection optical signal to be emitted to the target, and the received target reflected optical signal and the reference optical signal are beat by a balanced detector to obtain a measurement path beat signal; the frequency modulated continuous optical signal of the auxiliary path passes through a Mach-Zehnder interferometer with a fixed delay difference and then beats by a balanced detector to obtain an auxiliary path beat signal; then the auxiliary path beat signal and the measurement path beat signal are digitally processed: first, the frequency range of the measurement path beat signal is preliminarily searched out, and then the frequency of the measurement path beat signal is determined within the preliminarily searched frequency range using a linear frequency modulated z-transform method; at the same time, the phase noise in the auxiliary path beat signal is extracted; according to the frequency of the measurement path beat signal and the phase noise in the auxiliary path beat signal, the phase noise of the measurement path is estimated; finally, the obtained measurement path phase noise is compensated.

[0037] The technical solution of the present invention is further described in detail below through a specific embodiment:

[0038] This embodiment uses an arbitrary waveform generator to generate a triangular waveform voltage with a period of T as a modulation signal to control the laser to generate a linear frequency modulated continuous optical signal whose optical frequency changes with the applied voltage. The frequency variation curves of the transmitted signal and the received signal over time are shown in Figure 2 As shown in (a), the solid line is the transmitted signal and the dotted line is the received signal. The initial modulation frequency of the laser is f0, the modulation bandwidth is B, and the modulation period is T. Figure 2 (b) is the time-frequency diagram of the ideal beat signal. D The existence of the modulation period T, the frequencies obtained by the beat frequency in the upper and lower frequency modulation stages are not equal, respectively f b+ and f b- Then, the radial distance and speed of the target relative to the lidar can be obtained through these two frequencies:

[0039]

[0040] Where c is the speed of light in a vacuum environment, λ is the central wavelength of the laser, and τ c It is the delay between the transmitted signal and the received signal in the measurement path.

[0041] Since the analysis of the upper and lower frequency modulation stages is similar, in order to simplify the formula, we will only consider the upper frequency modulation stage. Within the range of half a modulation period (0, T / 2), the FMCW reference frequency f(t) can be expressed as:

[0042] f(t)=f0+γt,γ=2B / T (2)

[0043] Therefore, taking phase noise into account, the optical signal output by the tunable laser can be expressed as:

[0044]

[0045] In the formula, is the phase noise.

[0046] Then, the optical signal output by the laser is divided into two paths, a small part of which is introduced into a channel with a fixed delay τ r The Mach-Zehnder interferometer (MZI) is used as an auxiliary path, and most of the rest is used for target measurement. The auxiliary path is delayed by τ r The FMCW optical signal can be expressed as:

[0047]

[0048] The auxiliary MZI couples the two FMCW signals with fixed delays and then enters the photodetector beat frequency. After removing the DC term and high-frequency term, the beat frequency signal can be expressed as:

[0049]

[0050] Similarly, the beat frequency signal of the measurement path can also be expressed as:

[0051]

[0052] Next, the frequency range of the beat signal in the measurement path is estimated. First, the frequency range where the beat signal is located is searched. Based on the power spectrum density of the signal, the average power within a certain range can be obtained to avoid the error that may be caused by directly obtaining the maximum value of the spectrum. At the same time, this method realizes automatic frequency range estimation and does not require manual spectrum analysis. The location of the beat signal can be determined by comparing the average power size in different frequency ranges. s By sampling the beat frequency signal, I2(t) is rewritten into a discrete signal form I2(nT s ), where T s is the sampling time interval 1 / f s . Perform discrete Fourier transform (DFT) on a discrete beat frequency signal with N sampling points:

[0053]

[0054] The actual frequency corresponding to each frequency component of X(k) is f k =kf s / N. The power spectral density (PSD) is obtained from the DFT output and is expressed as:

[0055]

[0056] The signal frequency range search can adopt conventional algorithms such as binary search. In order to improve the search efficiency, the present invention further proposes an improved binary search method. The steps of searching the signal frequency range by the improved binary search method are as follows: first, determine the entire frequency band interval as [f1, f2], and divide it into three parts, and there is overlap between every two adjacent parts of the three parts; after the division, the width of each frequency band is the same as (f2-f1) / 2, and their starting frequencies decrease from high to low, and the starting frequency difference between every two adjacent frequency bands is (f2-f1) / 4. Therefore, the three frequency band intervals are [f1, f1 / 2+f2 / 2], [3f1 / 4+f2 / 4, f1 / 4+3f2 / 4], and [f1 / 2+f2 / 2, f2]; by performing S x (f k ) to perform trapezoidal numerical integration and calculate the average power of the three frequency bands respectively; select the frequency band with the largest average power to repeat the above operation, and gradually narrow the search range of the beat frequency through iteration until the width of the final selected partial frequency band meets the preset requirements.

[0057] Assume that the frequency range of the beat frequency signal is finally determined to be [f start ,f end ]. Next, the linear frequency modulation z-transform (CZT) method is used to estimate the beat frequency within the selected frequency range. CZT maps the input signal to an arbitrarily selected complex plane region, which means that higher-density data processing can be performed on certain key frequency bands, thereby improving the resolution within this region. In addition, CZT can enhance the analysis capability of high-frequency components. By adjusting the parameters, computing resources can be concentrated on specific frequency bands, thereby improving the recognition accuracy of these components. According to the part with higher linearity in the frequency modulated optical signal, that is, the middle part of the up and down frequency modulation stages, the beat signal of the corresponding time period is selected, because the frequency change in this time period is relatively gentle. According to the above method, N1 sampling points of the beat signal are selected for CZT, which can be expressed as:

[0058]

[0059] Where A is the complex starting point, W is the interval between adjacent sampling points, which can be expressed as:

[0060]

[0061] Assuming that the CZT peak position is at point k1, the corresponding peak frequency is:

[0062]

[0063] The phase noise can be extracted by digitally processing the auxiliary path beat signal. Since the MZI in the auxiliary path has a small delay difference, its beat signal is relatively less affected by the phase noise. In this case, the beat frequency can be regarded as the frequency where the spectrum peak is located after the discrete Fourier transform. Beat frequency γτ r It is known that the phase noise of the signal can be extracted through digital processing. The specific method is as follows:

[0064]

[0065] in unwrap[·],tan -1 [·], hilbert[·] represent phase unwrapping function, arc tangent function, and Hilbert function, respectively.

[0066] Afterwards, the phase noise extracted from the auxiliary path is The beat frequency roughly estimated from the measurement path Combined to estimate the phase noise of the measurement path

[0067] First, the phase noise of the measurement path can be written as follows:

[0068]

[0069] The first term of formula (13) can be obtained by summing the phase noise delay of the auxiliary path:

[0070]

[0071] in round[·] means rounding to the nearest integer.

[0072] The second term of formula (13) is regarded as a residual term. When the delay τ r When it is relatively small, and Considered as a linear relationship with respect to the delay, the residual term can be expressed as:

[0073]

[0074] Where p = (τ c -Nτ r ) / τr is an unknown number and can be estimated

[0075] Assume that the estimated phase noise is The measured path beat frequency signal is compared with the constructed compensation factor By multiplying, we can get the beat frequency signal of the measurement path after phase noise compensation, which is expressed as:

[0076]

[0077] According to formula (16), after the phase noise compensated signal undergoes Fourier transform, the beat frequency in the positive half spectrum is almost unaffected by the phase noise, and both the resolution and signal-to-noise ratio will be significantly improved.

[0078] In order to verify the technical effect of the present invention, the following experiments were performed:

[0079] First, a frequency modulated continuous wave laser radar ranging system was built. The specific structure is as follows: Figure 1 As shown. A distributed feedback laser with a line width of 200KHz is used as the light source, and the corresponding coherence length is about 250m (round-trip distance). The AWG generates a triangle wave signal with a period of 100us and an amplitude of 0-600mV as the modulation signal. The measured modulation bandwidth is 20GHz, and the corresponding distance resolution is 0.75cm. A 2m single-mode optical fiber is used as the MZI two-path optical path difference of the auxiliary path. Then, the improved binary search method is used to search the frequency range of the measurement path beat frequency signal, and the results are shown as follows Figure 3 As shown in the figure, the final frequency range is [1774MHz, 1784MHz]. Next, the CZT frequency estimation is performed on the beat signal within the above frequency range. The result is as follows: Figure 4 As shown, the estimated peak frequency is 1779.09 MHz.

[0080] On the other hand, the beat signal of the auxiliary path is digitally processed. First, the beat signal frequency is obtained by FFT, which is 3.7861MHz. Then, the phase noise is extracted according to formula (12), and then the phase noise is estimated by combining the beat frequency of the measurement path. According to formulas (14) and (15), N = 470, p = -0.1 is calculated. Finally, the beat signal of the measurement path is compensated, and the result is as follows: Figure 5 As shown in the figure, the coherence peak reappears, the signal-to-noise ratio is significantly improved, the spectrum peak frequency is 1778.83MHz, and the corresponding distance is 704.75m. The experimental results show that this scheme significantly improves the measurement distance in the FMCW lidar system, thereby realizing super-coherent length measurement. Figure 6As shown, the optimal solution obtained by the method of document [1] is still N = 470, p = -0.1. Therefore, compared with document [1], the technical solution of the present invention reduces the traversal process and greatly reduces the amount of calculation.

Claims

1. A method for compensating phase noise of a frequency modulated continuous wave laser radar, wherein the frequency modulated continuous wave laser radar divides a frequency modulated continuous optical signal into two paths: a measurement path and an auxiliary path; the frequency modulated continuous optical signal of the measurement path is divided into two paths, one path is used as a reference optical signal, and the other path is used as a detection optical signal to be emitted to a target, and the received target reflected optical signal is beat with the reference optical signal to obtain a measurement path beat signal; the frequency modulated continuous optical signal of the auxiliary path passes through a path with a fixed delay difference τ r The beat frequency is performed after the Mach-Zehnder interferometer to obtain the auxiliary path beat frequency signal; it is characterized in that, The phase noise of the measurement path is obtained by performing the following digital processing on the auxiliary path beat frequency signal and the measurement path beat frequency signal, and then the obtained measurement path phase noise is compensated: First, the frequency range of the measurement path beat frequency signal is preliminarily searched out, and then the linear frequency modulation z-transform method is used to determine the frequency of the measurement path beat frequency signal within the preliminarily searched frequency range. At the same time, the phase noise in the auxiliary path beat signal is extracted The phase noise of the measurement path is estimated according to the following formula: in, round[·] means rounding to the nearest integer, γτ r is the beat frequency of the auxiliary path beat signal, 2. The method for compensating phase noise of a frequency modulated continuous wave laser radar according to claim 1, characterized in that: The improved binary search method is used to preliminarily search for the frequency range of the beat frequency signal of the measurement path, as follows: the entire frequency band interval is divided into three parts, and there is overlap between every two adjacent parts of the three parts; the average power of the three parts is calculated and the part with the largest average power is selected to repeat the above process; iterate in sequence until the width of the final selected partial frequency band meets the preset requirements.

3. The FMCW laser radar phase noise compensation method according to claim 1, characterized in that: The phase noise of the obtained measurement path is compensated using the following method: Based on the estimated phase noise of the measurement path Constructing compensation factors Then use the compensation factor Multiplied by the measurement path beat frequency signal.

4. A frequency modulated continuous wave laser radar phase noise compensation device, wherein the frequency modulated continuous wave laser radar divides the frequency modulated continuous light signal into two paths: a measurement path and an auxiliary path; the frequency modulated continuous light signal of the measurement path is divided into two paths, one path is used as a reference light signal, and the other path is used as a detection light signal to be emitted to the target, and the received target reflected light signal is beat with the reference light signal to obtain the measurement path beat signal; the frequency modulated continuous light signal of the auxiliary path passes through a fixed delay difference τ r The beat frequency is performed after the Mach-Zehnder interferometer to obtain the auxiliary path beat frequency signal; it is characterized in that, The frequency modulated continuous wave laser radar phase noise compensation device obtains the phase noise of the measurement path by performing the following digital processing on the auxiliary path beat frequency signal and the measurement path beat frequency signal, and then compensates the obtained measurement path phase noise, specifically including: A frequency range search module is used to preliminarily search for the frequency range of the beat frequency signal of the measurement path; Frequency estimation module, used to determine the frequency of the beat signal of the measurement path within the frequency range preliminarily searched using the linear frequency modulation z-transform method Phase noise extraction module, used to extract the phase noise in the auxiliary path beat frequency signal The measurement path phase noise estimation module is used to estimate the phase noise of the measurement path according to the following formula in, round[·] means rounding to the nearest integer, γτ r is the beat frequency of the auxiliary path beat signal, The phase noise compensation module is used to compensate the phase noise of the obtained measurement path.

5. The FMCW laser radar phase noise compensation device as claimed in claim 4, characterized in that: The frequency range search module uses the improved binary search method to preliminarily search for the frequency range of the beat frequency signal of the measurement path, as follows: divide the entire frequency band into three parts, and there is overlap between every two adjacent parts of the three parts; calculate the average power of the three parts and select the part with the largest average power to repeat the above process; iterate in sequence until the width of the final selected partial frequency band meets the preset requirements.

6. The FMCW laser radar phase noise compensation device according to claim 4, characterized in that: The phase noise compensation module uses the following method to compensate the phase noise of the obtained measurement path: Constructing compensation factors Then use the compensation factor Multiplied by the measurement path beat frequency signal.

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