CN115171720A - Super-resolution multi-tone detection estimation method and device - Google Patents
Super-resolution multi-tone detection estimation method and device Download PDFInfo
- Publication number
- CN115171720A CN115171720A CN202210734111.XA CN202210734111A CN115171720A CN 115171720 A CN115171720 A CN 115171720A CN 202210734111 A CN202210734111 A CN 202210734111A CN 115171720 A CN115171720 A CN 115171720A
- Authority
- CN
- China
- Prior art keywords
- signals
- signal
- complex vector
- amplitude
- estimation
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Pending
Links
- 238000000034 method Methods 0.000 title claims abstract description 48
- 238000001514 detection method Methods 0.000 title claims abstract description 38
- 239000011159 matrix material Substances 0.000 claims abstract description 44
- 239000013598 vector Substances 0.000 claims abstract description 41
- 238000012545 processing Methods 0.000 claims abstract description 11
- 238000005070 sampling Methods 0.000 claims description 9
- 239000000654 additive Substances 0.000 claims description 3
- 230000000996 additive effect Effects 0.000 claims description 3
- 238000004364 calculation method Methods 0.000 claims description 3
- 238000001228 spectrum Methods 0.000 abstract description 9
- 238000013461 design Methods 0.000 abstract description 4
- 238000010586 diagram Methods 0.000 description 3
- 238000003672 processing method Methods 0.000 description 2
- 238000004891 communication Methods 0.000 description 1
- 238000000354 decomposition reaction Methods 0.000 description 1
- 238000005516 engineering process Methods 0.000 description 1
- 238000013178 mathematical model Methods 0.000 description 1
- 238000005259 measurement Methods 0.000 description 1
- 238000012986 modification Methods 0.000 description 1
- 230000004048 modification Effects 0.000 description 1
Images
Classifications
-
- G—PHYSICS
- G10—MUSICAL INSTRUMENTS; ACOUSTICS
- G10L—SPEECH ANALYSIS TECHNIQUES OR SPEECH SYNTHESIS; SPEECH RECOGNITION; SPEECH OR VOICE PROCESSING TECHNIQUES; SPEECH OR AUDIO CODING OR DECODING
- G10L25/00—Speech or voice analysis techniques not restricted to a single one of groups G10L15/00 - G10L21/00
- G10L25/03—Speech or voice analysis techniques not restricted to a single one of groups G10L15/00 - G10L21/00 characterised by the type of extracted parameters
- G10L25/21—Speech or voice analysis techniques not restricted to a single one of groups G10L15/00 - G10L21/00 characterised by the type of extracted parameters the extracted parameters being power information
-
- G—PHYSICS
- G10—MUSICAL INSTRUMENTS; ACOUSTICS
- G10L—SPEECH ANALYSIS TECHNIQUES OR SPEECH SYNTHESIS; SPEECH RECOGNITION; SPEECH OR VOICE PROCESSING TECHNIQUES; SPEECH OR AUDIO CODING OR DECODING
- G10L25/00—Speech or voice analysis techniques not restricted to a single one of groups G10L15/00 - G10L21/00
- G10L25/03—Speech or voice analysis techniques not restricted to a single one of groups G10L15/00 - G10L21/00 characterised by the type of extracted parameters
- G10L25/18—Speech or voice analysis techniques not restricted to a single one of groups G10L15/00 - G10L21/00 characterised by the type of extracted parameters the extracted parameters being spectral information of each sub-band
-
- G—PHYSICS
- G10—MUSICAL INSTRUMENTS; ACOUSTICS
- G10L—SPEECH ANALYSIS TECHNIQUES OR SPEECH SYNTHESIS; SPEECH RECOGNITION; SPEECH OR VOICE PROCESSING TECHNIQUES; SPEECH OR AUDIO CODING OR DECODING
- G10L25/00—Speech or voice analysis techniques not restricted to a single one of groups G10L15/00 - G10L21/00
- G10L25/27—Speech or voice analysis techniques not restricted to a single one of groups G10L15/00 - G10L21/00 characterised by the analysis technique
-
- G—PHYSICS
- G10—MUSICAL INSTRUMENTS; ACOUSTICS
- G10L—SPEECH ANALYSIS TECHNIQUES OR SPEECH SYNTHESIS; SPEECH RECOGNITION; SPEECH OR VOICE PROCESSING TECHNIQUES; SPEECH OR AUDIO CODING OR DECODING
- G10L25/00—Speech or voice analysis techniques not restricted to a single one of groups G10L15/00 - G10L21/00
- G10L25/48—Speech or voice analysis techniques not restricted to a single one of groups G10L15/00 - G10L21/00 specially adapted for particular use
- G10L25/51—Speech or voice analysis techniques not restricted to a single one of groups G10L15/00 - G10L21/00 specially adapted for particular use for comparison or discrimination
Landscapes
- Engineering & Computer Science (AREA)
- Physics & Mathematics (AREA)
- Computational Linguistics (AREA)
- Signal Processing (AREA)
- Health & Medical Sciences (AREA)
- Audiology, Speech & Language Pathology (AREA)
- Human Computer Interaction (AREA)
- Acoustics & Sound (AREA)
- Multimedia (AREA)
- Spectroscopy & Molecular Physics (AREA)
- Measurement Of Velocity Or Position Using Acoustic Or Ultrasonic Waves (AREA)
Abstract
The invention discloses a super-resolution multi-tone detection estimation method and a device, wherein the method comprises the following steps: obtaining a covariance matrix of the complex vector based on the continuously and uniformly sampled complex vector; the complex vector comprises a plurality of dot frequency signals; calculating an AR coefficient according to the covariance matrix of the complex vector; obtaining the amplitudes of a plurality of signals by adopting an MVDR method based on the AR coefficient; from the amplitudes of the plurality of signals, a signal satisfying an amplitude threshold requirement is detected. The invention reduces the design complexity and the software hardware resource requirement on the premise of ensuring the processing performance by the optimized design of the super-resolution signal detection and estimation processing based on the parameterized spectrum estimation, so that the super-resolution signal detection and estimation can be realized by engineering, and the invention has strong practical value.
Description
Technical Field
The invention relates to the technical field of signal detection, in particular to a super-resolution multi-tone detection estimation method and device.
Background
The detection and estimation of the dot frequency signals are general technologies with wide application, and have the same equivalent mathematical model in various application fields of communication, radar, sonar navigation and the like, such as pulse Doppler radar target detection and speed measurement, arrival angle estimation of an airspace uniform linear array and the like.
The difficulty in detecting and estimating parameters of dot frequency signals is that when multiple independent signals exist simultaneously, the signals with frequencies close to each other are difficult to distinguish due to observation aperture. The conventional resolution, the rayleigh resolution interval, determined in a non-parametric estimation technique. For line spectrum parameter estimation of polyphonic signals and the like, the parameterized spectrum estimation method can obtain processing performance exceeding conventional resolution.
In the prior art, one type is non-parametric spectrum estimation (see non-patent document 1), the technical resolution performance cannot exceed the rayleigh resolution, the method is mainly applied to the situation that the resolution requirement is not high, and various improvement measures are usually taken to improve the estimation performance at the cost of reducing the resolution.
Another type of prior art is a parametric spectrum estimation technique (see non-patent document 1), such as an AR parameter estimation method, a MUSIC method, an ESPRIT method, and the like. Due to the fact that line spectrum assumption is carried out on the frequency spectrum of the signal, parametric estimation can better process multi-tone signals, and more accurate estimation of frequency is obtained. However, the pseudo spectrum calculated by the parameterization method has the problem that the signal amplitude is difficult to accurately estimate, and the detection performance of the signal is severely limited. Meanwhile, the processing method comprises complex operations and heavy processing such as matrix characteristic decomposition, frequency sampling search and the like, and the engineering realization difficulty is greatly increased.
Reference list
Non-patent document 1: he shou, xia Wei, modern digital signal processing and its applications, qinghua university Press.
Disclosure of Invention
In view of this, the present invention provides a super-resolution multi-tone detection and estimation method and device, which solve the problem that super-resolution signal detection and estimation are difficult to implement in engineering.
The invention discloses a super-resolution multi-tone signal detection and estimation method, which comprises the following steps:
step 1: continuously and uniformly sampling the polyphonic signals to obtain complex vectors; wherein, the multi-tone signal is formed by mixing a plurality of dot frequency signals;
step 2: calculating an AR coefficient according to the covariance matrix of the complex vector;
and 3, step 3: obtaining the amplitudes of a plurality of signals by adopting an MVDR method based on the AR coefficient;
and 4, step 4: from the amplitudes of the plurality of signals, a signal satisfying an amplitude threshold requirement is detected.
Further, the complex vector contains additive independent complex gaussian noise; and the signal meeting the amplitude threshold requirement is the dot frequency signal in the multi-tone signal.
Further, the step 1 comprises:
under the conditions of limited aperture and few dot frequency signals, continuously and uniformly sampling the polyphonic signals to form a complex vector;
the process of obtaining the covariance matrix of the complex vector is as follows:
and estimating a signal covariance matrix by using the complex vector by adopting a forward and backward method.
Further, the estimating a signal covariance matrix by using the complex vector by using a forward-backward method includes:
expressing the complex vector as X = [ X ] 1 ，x 2 ，...，x N ] T The forward matrix is:
wherein, A f Is a forward matrix, x i Is the i-th element of the complex vector,
is x i N is the number of elements of the complex vector;
rearranging elements of the forward matrix to obtain a backward matrix:
wherein A is b Is a backward matrix, a f (i, j) is the ith row in the forward matrixj columns of elements;
calculating a covariance matrix:
wherein A is a covariance matrix.
Further, the step 2 comprises:
the AR coefficients were solved using the Yule-Walker equation:
wherein, a 1 、a 2 、a 3 Respectively, the calculated AR coefficients, A is a covariance matrix,
is the variance of the input signal of the AR model,
has a value of A -1 [1，0，0，0] T The first element of (1).
Further, the step 3 comprises:
step 31: calculating normalized frequencies of the plurality of signals using the AR coefficients;
step 32: on the basis of the normalized frequency, the MVDR method is adopted to respectively solve the amplitudes of the multiple signals.
Further, the step 31 includes:
the AR coefficients are used to establish the equation:
1+a 1 x+a 2 x 2 +a 3 x 3 ＝0 (5)
directly solving the equation by using a 1-element 3-order equation analytic solution formula to obtain 3 corresponding phases, namely normalized frequencies of a plurality of signals, and the module values are corresponding amplitudes,
wherein phi k Is the phase of the kth root, m k For the amplitude of the kth root, k =1,2,3.
Further, the step 32 includes:
using the MVDR algorithm, the amplitude estimation error is reduced on the basis of the frequency estimation obtained by AR processing, i.e.
Wherein p is k Amplitude estimation for the kth point frequency signal;
and determining the 2 signals with the largest amplitude values in the plurality of signals as the signals to be detected.
Further, the step 4 comprises:
setting an amplitude detection threshold lambda according to the actual application requirement, and taking the signal with the amplitude value larger than the amplitude detection threshold lambda in the signal to be detected as the final detection result.
The invention also discloses a super-resolution multi-tone detection and estimation device, which comprises:
the acquisition module is used for continuously and uniformly sampling the multi-tone signal to obtain a complex vector; wherein, the multi-tone signal is formed by mixing a plurality of dot frequency signals;
the calculation module is used for calculating an AR coefficient according to the covariance matrix of the complex vector;
the amplitude module is used for obtaining the amplitudes of a plurality of signals by adopting an MVDR method based on the AR coefficient;
and the detection module is used for detecting the dot frequency signals meeting the requirement of the amplitude threshold from the amplitudes of the signals.
Due to the adoption of the technical scheme, the invention has the following advantages: the invention is suitable for super-resolution detection and estimation under the conditions of limited aperture and extremely small number of point frequency signals, reduces the design complexity and the software hardware resource requirement on the premise of ensuring the processing performance through the optimized design of super-resolution signal detection and estimation processing based on parametric spectrum estimation, solves the problem that the super-resolution signal detection and estimation are difficult to realize in engineering, and has very strong practical value.
Drawings
In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the drawings needed to be used in the description of the embodiments are briefly introduced below, and it is obvious that the drawings in the following description are only some embodiments described in the embodiments of the present invention, and it is obvious for those skilled in the art that other drawings can be obtained according to the drawings.
FIG. 1 is a schematic flow chart of a super-resolution multi-tone detection estimation method according to an embodiment of the present invention;
FIG. 2 is a diagram illustrating a relationship between a detection threshold and a detection false alarm according to an embodiment of the present invention;
FIG. 3 is a schematic diagram of a correct resolution performance comparison according to an embodiment of the present invention;
FIG. 4 is a diagram illustrating a comparison of signal frequency estimation errors under correct resolution conditions according to an embodiment of the present invention.
Detailed Description
The present invention will be further described with reference to the accompanying drawings and examples, it being understood that the examples described are only some of the examples and are not intended to limit the invention to the embodiments described herein. All other embodiments available to those of ordinary skill in the art are intended to be within the scope of the embodiments of the present invention.
Referring to fig. 1, the present invention provides an embodiment of a method for detecting and estimating super-resolution multitone signals, which includes the following steps:
step 1: continuously and uniformly sampling the polyphonic signals to obtain complex vectors; the multi-tone signal is formed by mixing a plurality of dot frequency signals;
step 2: calculating an AR coefficient according to the covariance matrix of the complex vector;
and step 3: obtaining the amplitudes of a plurality of signals by adopting an MVDR method based on the AR coefficient;
and 4, step 4: from the amplitudes of the plurality of signals, a signal is detected that meets an amplitude threshold requirement.
In this embodiment, the complex vector contains additive independent complex gaussian noise; the signal meeting the amplitude threshold requirement is the dot frequency signal in the multi-tone signal.
In this embodiment, step 1 includes:
under the conditions of limited aperture and few dot frequency signals, multi-tone signals are continuously and uniformly sampled to form a complex vector;
the process of obtaining the covariance matrix of the complex vector is as follows:
and estimating a signal covariance matrix by using the complex vector by adopting a forward and backward method.
In this embodiment, estimating the signal covariance matrix by using the complex vector by using a forward-backward method includes:
representing a complex vector as x = [ x ] 1 ，x 2 ，...，x N ] T The forward matrix is:
wherein A is f Is a forward matrix, x i Is the i-th element of the complex vector,
is x i N is the number of elements of the complex vector;
rearranging elements of the forward matrix to obtain a backward matrix:
wherein, A b Is a backward matrix, a f (i, j) is the ith row and the jth column element in the forward matrix;
calculating a covariance matrix:
wherein A is a covariance matrix.
In this embodiment, step 2 includes:
solving the AR coefficients using the Yule-Walker equation:
wherein, a 1 、a 2 、a 3 Respectively, the calculated AR coefficients, A is a covariance matrix,
is the variance of the input signal of the AR model,
has a value of A -1 [1，0，0，0] T The first element of (a).
In this embodiment, step 3 includes:
step 31: calculating normalized frequencies of the plurality of signals using the AR coefficients;
step 32: on the basis of the normalized frequency, the MVDR method is adopted to respectively solve the amplitudes of the multiple signals.
In this embodiment, step 31 includes:
the AR coefficients are used to establish the equation:
1+a 1 x+a 2 x 2 +a 3 x 3 ＝0 (5)
directly solving the equation by using a 1-element 3-order equation analytic solution formula to obtain 3 corresponding phases, namely normalized frequencies of a plurality of signals, and the module values are corresponding amplitudes,
wherein phi k Is the phase of the kth root, m k For the amplitude of the kth root, k =1,2,3.
In this embodiment, step 32 includes:
using the MVDR algorithm, the amplitude estimation error is reduced on the basis of the frequency estimation obtained by AR processing, i.e.
Wherein p is k Amplitude estimation for a kth point frequency signal;
and determining the 2 signals with the largest amplitude values in the plurality of signals as the signals to be detected.
In this embodiment, step 4 includes:
and setting an amplitude detection threshold lambda according to the actual application requirement, and taking the signal with the amplitude value larger than the amplitude detection threshold lambda in the signal to be detected as the final detection result.
The invention also provides an embodiment of the super-resolution multi-tone detection and estimation device, which comprises:
the acquisition module is used for continuously and uniformly sampling the multi-tone signal to obtain a complex vector; wherein, the polyphonic signal is formed by mixing a plurality of dot frequency signals;
the calculation module is used for calculating the AR coefficient according to the covariance matrix of the complex vector;
the amplitude module is used for obtaining the amplitudes of the signals by adopting an MVDR method based on the AR coefficient;
and the detection module is used for detecting the dot frequency signal meeting the requirement of the amplitude threshold from the amplitudes of the plurality of signals.
To facilitate understanding, a more specific embodiment of the invention is given:
taking N =8 and N =12 as an example, when the noise power in the input complex vector is 1, the relationship between the detection threshold and the detection false alarm is shown in fig. 2.
For example, with N =8, 2 frequency-close signals are set, where the smaller signal sample signal-to-noise ratio is 14dB, the normalized frequency is 0, the larger signal sample signal-to-noise ratio is 20dB, and the normalized frequency is from 0 to 0.25. The invention and the conventional periodogram method are used for processing and estimating signals, and the false alarm probability of both the two methods is 10 -3 The results are shown in FIGS. 3 and 4. As can be seen from the results, the super-resolution processing method provided by the invention has significant improvement in detection performance and estimation accuracy compared with the conventional periodogram method.
Finally, it should be noted that: the above embodiments are only for illustrating the technical solutions of the present invention and not for limiting the same, and although the present invention is described in detail with reference to the above embodiments, those of ordinary skill in the art should understand that: modifications and equivalents may be made to the embodiments of the invention without departing from the spirit and scope of the invention, which is to be covered by the claims.
Claims (10)
1. A super-resolution multi-tone signal detection and estimation method is characterized by comprising the following steps:
step 1: continuously and uniformly sampling the polyphonic signals to obtain complex vectors; wherein, the multi-tone signal is formed by mixing a plurality of dot frequency signals;
step 2: calculating an AR coefficient according to the covariance matrix of the complex vector;
and step 3: obtaining the amplitudes of a plurality of signals by adopting an MVDR method based on the AR coefficient;
and 4, step 4: from the amplitudes of the plurality of signals, a signal is detected that meets an amplitude threshold requirement.
2. The method of claim 1, wherein the complex vector contains additive independent complex gaussian noise; and the signal meeting the amplitude threshold requirement is the dot frequency signal in the multi-tone signal.
3. The method of claim 1, wherein step 1 comprises:
under the conditions of limited aperture and few dot frequency signals, continuously and uniformly sampling the polyphonic signals to form a complex vector;
the process of obtaining the covariance matrix of the complex vector is as follows:
and estimating a signal covariance matrix by using the complex vector by adopting a forward and backward method.
4. The method of claim 3, wherein estimating a signal covariance matrix from the complex vector using a forward-backward approach comprises:
representing a complex vector as x = [ x ] 1 ,x 2 ,...,x N ] T The forward matrix is:
wherein A is f Is a forward matrix, x i Is the i-th element of the complex vector,
is x i N is the number of elements of the complex vector;
rearranging elements of the forward matrix to obtain a backward matrix:
wherein A is b Is a backward matrix, a f (i, j) is the ith row and the jth column element in the forward matrix;
calculating a covariance matrix:
wherein A is a covariance matrix.
5. The method of claim 1, wherein the step 2 comprises:
the AR coefficients were solved using the Yule-Walker equation:
wherein, a 1 、a 2 、a 3 Respectively, the calculated AR coefficients, A is a covariance matrix,
is the variance of the input signal of the AR model,
has a value of A -1 [1,0,0,0] T The first element of (1).
6. The method of claim 5, wherein step 3 comprises:
step 31: calculating normalized frequencies of the plurality of signals using the AR coefficients;
step 32: on the basis of the normalized frequency, the MVDR method is adopted to respectively solve the amplitudes of the multiple signals.
7. The method of claim 6, wherein the step 31 comprises:
the AR coefficients are used to establish the equation:
1+a 1 x+a 2 x 2 +a 3 x 3 ＝0 (5)
directly solving the equation by using a 1-element 3-order equation analytic solution formula to obtain 3 corresponding phases, namely normalized frequencies of a plurality of signals, and the module values are corresponding amplitudes,
wherein phi is k Is the phase of the kth root, m k For the amplitude of the kth root, k =1,2,3.
8. The method of claim 7, wherein the step 32 comprises:
using the MVDR algorithm, the amplitude estimation error is reduced on the basis of the frequency estimation obtained by AR processing, i.e.
Wherein p is k Amplitude estimation for the kth point frequency signal;
and determining the 2 signals with the maximum amplitude values in the plurality of signals as the signals to be detected.
9. The method of claim 8, wherein the step 4 comprises:
setting an amplitude detection threshold lambda according to the actual application requirement, and taking the signal with the amplitude value larger than the amplitude detection threshold lambda in the signal to be detected as the final detection result.
10. A super-resolution multi-tone detection estimation device, comprising:
the acquisition module is used for continuously and uniformly sampling the multi-tone signal to obtain a complex vector; wherein the multi-tone signal is formed by mixing a plurality of dot frequency signals;
the calculation module is used for calculating an AR coefficient according to the covariance matrix of the complex vector;
the amplitude module is used for obtaining the amplitudes of a plurality of signals by adopting an MVDR method based on the AR coefficient;
and the detection module is used for detecting the dot frequency signals meeting the requirement of the amplitude threshold from the amplitudes of the signals.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202210734111.XA CN115171720A (en) | 2022-06-27 | 2022-06-27 | Super-resolution multi-tone detection estimation method and device |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202210734111.XA CN115171720A (en) | 2022-06-27 | 2022-06-27 | Super-resolution multi-tone detection estimation method and device |
Publications (1)
| Publication Number | Publication Date |
|---|---|
| CN115171720A true CN115171720A (en) | 2022-10-11 |
Family
ID=83487584
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN202210734111.XA Pending CN115171720A (en) | 2022-06-27 | 2022-06-27 | Super-resolution multi-tone detection estimation method and device |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN115171720A (en) |
-
2022
- 2022-06-27 CN CN202210734111.XA patent/CN115171720A/en active Pending
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| CN110208785B (en) | Radar maneuvering target rapid detection method based on robust sparse fractional Fourier transform | |
| CN111628790B (en) | High-precision anti-interference method and device based on interference bandwidth detection | |
| CN111610503B (en) | Linear frequency modulation signal parameter estimation method based on improved LVD | |
| CN112630784B (en) | Plane array amplitude-phase error correction method based on convex optimization and neural network | |
| US20190020504A1 (en) | Phase-Modulated Signal Parameter Estimation Using Streaming Calculations | |
| CN109471063B (en) | Uniform linear array high-resolution direction-of-arrival estimation method based on delayed snapshot | |
| CN112162152B (en) | Sine wave coherent pulse train signal frequency estimation method based on phase straight line fitting | |
| CN111624573A (en) | Time domain self-adaptive target detection method under sea clutter background | |
| CN105158751A (en) | Acoustic vector array fast DOA (Direction of Arrival) estimation method | |
| CN110716203B (en) | Time-frequency analysis and tracking method of passive sonar target | |
| CN111913155A (en) | Two-dimensional DOA estimation method based on array radar | |
| CN110196407B (en) | Single-vector hydrophone signal incoming wave direction estimation method based on frequency estimation | |
| CN111175727B (en) | Method for estimating orientation of broadband signal based on conditional wave number spectral density | |
| CN109682492B (en) | Frequency estimation method based on frequency domain Gaussian fitting | |
| CN107728104A (en) | A kind of improved satellite navigation interference direction-finding method | |
| US5610612A (en) | Method for maximum likelihood estimations of bearings | |
| US11444643B2 (en) | Signal frequency and bandwidth estimation using a learned filter pair response | |
| CN111007473B (en) | High-speed weak target detection method based on distance frequency domain autocorrelation function | |
| CN107315714A (en) | One kind is deconvoluted the Power Spectrum Estimation Method | |
| CN115171720A (en) | Super-resolution multi-tone detection estimation method and device | |
| CN112444786A (en) | Method and device for acquiring reference noise floor, target detection method, target detection device and radar system | |
| CN110808929A (en) | Real-complex conversion type signal-to-noise ratio estimation algorithm of subtraction strategy | |
| CN111722178B (en) | Far-field narrow-band signal incoming wave direction estimation method based on numerical solution of directivity model | |
| CN108020818A (en) | A kind of sine pulse signal distance measuring method under noise based on sliding DFT | |
| US8867862B1 (en) | Self-optimizing analysis window sizing method |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination |