KR20210133684A - Method for simulating underwater sound transmission channel based on eigenray tracing - Google Patents

Abstract

A method for simulating an underwater acoustic propagation channel by an underwater acoustic propagation channel simulation device according to an embodiment includes the steps of deriving an eigenray solution for a plurality of eigenray paths between a sound source and a receiver, and deriving a finite impulse response including information on an underwater acoustic propagation channel by approximating the derived eigenray solution to a discrete time domain. The method for simulating an underwater acoustic propagation channel according to the present invention can minimize an error based on an eigenray analysis technique that can calculate time delays of multiple paths in a time domain.

Description

Method for simulating underwater sound transmission channel using sound path

The present invention relates to a method for simulating a hydroacoustic transmission channel using an eigenray path.

A sonar is a device that detects an underwater target by using sound waves in the water, so the hydroacoustic transmission channel is an important factor influencing the performance of the sonar. However, since the underwater acoustic transmission channel is affected by various environmental factors such as sea level and sea floor boundary conditions, the composition of the sea floor, and water temperature distribution, it is easy to simulate the measurement signal of the sonar according to the underwater acoustic transmission channel in advance. not. Therefore, it is difficult to sufficiently verify the sound wave transmission channel similar to the real environment in the design stage of the sonar, and it is common to perform the verification in the high-cost test and evaluation stage including the sea test.

In particular, the hydroacoustic transmission channel is often modeled as a time harmonic function in the frequency domain, so it is difficult to use it when simulating a wideband time-series signal except for some narrowband signals. In addition, in order to perform simulation using a computer, it must be possible to express in a discrete-time system. Therefore, a discrete-time modeling technique that reflects the underwater sound wave transmission environment is required.

Korean Patent Publication No. 10-1502408 (published on March 9, 2015)

According to an embodiment, a time domain approximation and simulation method capable of minimizing an error based on a eigenline analysis technique in which the time delay of multiple paths in the time domain can be calculated is provided.

The problems to be solved of the present invention are not limited to those mentioned above, and other problems to be solved that are not mentioned will be clearly understood by those of ordinary skill in the art to which the present invention belongs from the following description.

A method of simulating an underwater acoustic transmission channel by an underwater acoustic transmission channel simulation device according to a first aspect comprises the steps of deriving an eigenray solution for a plurality of eigenray paths between a sound source and a receiver, and the derived eigenray and deriving a finite impulse response including information of the hydroacoustic transmission channel by approximating the solution to the discrete time domain.

According to a second aspect, a computer readable recording medium storing a computer program comprises: when the computer program is executed by a processor, deriving a unique sound line solution for a plurality of natural sound line paths between a sound source and a receiver; Instructions for causing the processor to perform a hydroacoustic transmission channel simulation method, which includes deriving a finite impulse response including information on the hydroacoustic transmission channel by approximating the derived eigenline solution to the discrete time domain. .

According to a third aspect, when a computer program stored in a computer-readable recording medium is executed by a processor, deriving a unique sound line solution for a plurality of natural sound line paths between a sound source and a receiver; and instructions for causing the processor to perform a hydroacoustic channel simulation method including deriving a finite impulse response including information on the hydroacoustic channel by approximating the solution to the discrete time domain.

According to an embodiment, a time-domain approximation and simulation method capable of minimizing an error based on a eigenline analysis technique in which the time delay of multiple paths in the time domain can be calculated is provided. In this way, by simulating an underwater sound wave transmission channel reflecting the underwater physical environment (sonic profile, boundary topography and characteristics, etc.), it can be utilized in a simulator for sonar performance verification.

1 is a flowchart illustrating a method for simulating an underwater acoustic transmission channel by an underwater acoustic transmission channel simulation apparatus according to an embodiment of the present invention.
2 is a diagram illustrating a simulation process according to a method for simulating an underwater acoustic transmission channel according to an embodiment of the present invention.
3 is a diagram illustrating a high-speed convolution operation for generating a simulated sound source signal according to an embodiment of the present invention.
4 is a diagram illustrating a frequency response of a phase shift filter designed according to an embodiment of the present invention.
5 is a diagram illustrating a frequency response of a volume loss and phase shift filter designed according to an embodiment of the present invention.
6 is a diagram illustrating a frequency response of a fractional time delay filter designed according to an embodiment of the present invention.
7 is a diagram illustrating a finite impulse response modeling result of an underwater acoustic transmission channel using a natural sound line analysis result according to an embodiment of the present invention.

Advantages and features of the present invention and methods of achieving them will become apparent with reference to the embodiments described below in conjunction with the accompanying drawings. However, the present invention is not limited to the embodiments disclosed below, but may be implemented in various different forms, and only these embodiments allow the disclosure of the present invention to be complete, and common knowledge in the art to which the present invention pertains It is provided to fully inform those who have the scope of the invention, and the present invention is only defined by the scope of the claims.

Terms used in this specification will be briefly described, and the present invention will be described in detail.

The terms used in the present invention have been selected as currently widely used general terms as possible while considering the functions in the present invention, but these may vary depending on the intention or precedent of a person skilled in the art, the emergence of new technology, and the like. In addition, in a specific case, there is a term arbitrarily selected by the applicant, and in this case, the meaning will be described in detail in the description of the corresponding invention. Therefore, the term used in the present invention should be defined based on the meaning of the term and the overall content of the present invention, rather than the name of a simple term.

In the entire specification, when a part 'includes' a certain component, it means that other components may be further included, rather than excluding other components, unless otherwise stated.

Hereinafter, with reference to the accompanying drawings, embodiments of the present invention will be described in detail so that those of ordinary skill in the art can easily carry out the embodiments of the present invention. And in order to clearly explain the present invention in the drawings, parts irrelevant to the description will be omitted.

1 is a flowchart for explaining a method for simulating an underwater acoustic transmission channel by an underwater acoustic transmission channel simulation apparatus according to an embodiment of the present invention, and FIG. 2 is a simulation according to a method for simulating an underwater acoustic transmission channel according to an embodiment of the present invention A diagram illustrating the process. A simulation device capable of performing such a method for simulating the hydroacoustic transmission channel may be a device (eg, a computer, etc.) including a computing means such as a microprocessor.

Referring to FIGS. 1 and 2 , the method for simulating an underwater acoustic transmission channel includes deriving an eigenray solution for a plurality of eigenray paths between a sound source and a receiver ( S110 ). 2 shows an example of using Bellhop among known software for deriving an intrinsic sound line solution.

The method further includes a step (S120) of deriving a finite impulse response including information of an underwater acoustic transmission channel by approximating the eigenline solution derived in step S110 to a discrete time domain.

Here, the step of deriving the finite impulse response (S120) is the step of designing an approximation filter for each eigenline that can minimize the error when approximating the eigenline solution in the discrete time domain (S121) and utilizes the approximation filter for each eigenline and approximating the intrinsic sound line solution (S122). FIG. 2 shows an example of using a Finite Impulse Response (FIR) filter including a phase and loss approximation filter and a fractional time delay approximation filter as an approximation filter for each sound line.

3 is a diagram illustrating a high-speed convolution operation for generating a simulated sound source signal according to an embodiment of the present invention, FIG. 4 is a diagram illustrating a frequency response of a phase shift filter designed according to an embodiment of the present invention, and FIG. 5 is It is a diagram showing the frequency response of a volume loss and phase shift filter designed according to an embodiment of the present invention, FIG. 6 is a diagram showing the frequency response of a fractional time delay filter designed according to an embodiment of the present invention, and FIG. 7 is the present invention It is a diagram showing a finite impulse response modeling result of an underwater acoustic transmission channel using the analysis result of a natural sound line according to an embodiment of

Hereinafter, a method of simulating an underwater acoustic transmission channel by an underwater acoustic transmission channel simulation device will be described in detail with reference to FIGS. 1 to 7 .

The present invention simulates the hydroacoustic channel by approximating the time-invariant discrete-time finite impulse response from the information of the natural sound line calculated through the natural sound line analysis in which the multi-path time delay of the hydroacoustic transmission channel can be calculated. In order to apply this approximation technique, it is first necessary to obtain a sound line solution given as a high-frequency approximate solution of the wave equation describing the sound wave propagation phenomenon under a physical constraint environment. This is obtained by solving the Eikonal equation and the transport equation as in Equations 1 and 2 below under boundary conditions.

(수학식 1)

(Equation 1)

(수학식 2)

(Equation 2)

가 얻어질 수 있으며, 각각의 음선은 크기

, 위상

, 도달 시간지연

의 정보를 포함한다. 이로써, 음원과 수신기 사이의 다수의 고유 음선 경로에 대하여 고유 음선해를 도출하였다(S110).The solution of the above equation is generally not obtained analytically under complex boundary conditions and sound velocity structures, and various numerical analysis methods can be applied. It is also possible to obtain a unique sound ray solution by using software published on the Internet, such as Bellhop. On the other hand, there are multiple eigenline paths between a given sound source and receiver,

can be obtained, and each sound line is

, Phase

, arrival time delay

includes information on As a result, a eigenline solution was derived for a plurality of eigenline paths between the sound source and the receiver (S110).

을 수식으로 표현하면 아래의 수학식 3과 같다(S120).Since the intrinsic sound line solution derived in step S110 is obtained through Equation 1, which is a continuous-time equation, it cannot be directly applied to the discrete-time system, and therefore, it is necessary to go through a process of approximating it to the discrete-time domain. Finite impulse response derived by including all information of the underwater acoustic transmission channel obtained as a result of this approximation

When expressed as a formula, it is as in Equation 3 below (S120).

(수학식 3)

(Equation 3)

: 샘플 인덱스,

: 고유 음선 개수,

: 콘볼루션 연산, round(): 반올림 연산,

: i번째 고유 음선의 위상 및 손실 근사 필터,

: i번째 고유 음선의 소수 시간지연(

, fractional delay) 근사 필터,

의 필터 차수,

의 필터 차수)(only,

: sample index,

: number of distinct tones,

: convolution operation, round(): rounding operation,

: Phase and loss approximation filter of the ith eigenline,

: Decimal time delay of the i-th unique tone (

, fractional delay) approximation filter,

filter order of

filter order of )

을 모의할 수 있다. 콘볼루션 연산은 교환(commute)되기 때문에 어떤 순서로 실행하더라도 무관하며, 참고로 필터 차수가 긴 경우의 콘볼루션 연산은 신호의 분할과 FFT를 활용한 도 3 및 아래의 수학식 4와 같은 주파수 영역 연산(overlap add)으로 효율적으로 계산할 수 있다.The discrete-time signal received from the sonar by convolution of an arbitrary sound source signal and a finite impulse response representing an underwater acoustic channel

can be simulated. Since the convolution operation is commuted, it does not matter in which order it is executed. For reference, the convolution operation in the case of a long filter order is in the frequency domain as shown in FIG. 3 and Equation 4 below using signal division and FFT. It can be computed efficiently with an overlap add operation.

(수학식 4)

(Equation 4)

: 음원의 신호,

,

의 필터 차수)(only,

: signal of sound source,

,

filter order of )

On the other hand, when the natural sound line solution is derived through step S110, a finite impulse response including the information of the underwater acoustic transmission channel is derived based on the derived natural sound line solution (S120). To this end, an eigenphone-by-tone approximation filter that can minimize the error when approximating the eigenphone solution in the discrete time domain is designed (S121), and after approximating the eigenline solution using the designed eigenline approximation filter, the finite impulse response can be derived (S122).

을 구성하는 고유 음선별 근사 필터인

,

은 다음과 같이 얻어질 수 있다.Finite impulse response of the hydroacoustic channel given by Equation 3

The approximation filter for each distinct note that composes

,

can be obtained as follows.

는 각각의 고유 음선의 주파수 영역 진폭 및 위상인

에 대한 근사를 나타낸다. 이러한 주파수 영역에서 임의의 위상을 가지는 신호는, 원래 신호와 위상이

천이된 힐버트 변환(Hilbert transform) 신호의 주파수 영역의 가중 합으로 표현 가능하다. 따라서 필터

을 이용하여 힐버트 변환의 근사가 용이하여야 한다.first of all

is the frequency domain amplitude and phase of each distinct sound line.

represents an approximation to A signal having an arbitrary phase in this frequency domain is out of phase with the original signal.

It can be expressed as a weighted sum of the frequency domain of the shifted Hilbert transform signal. So filter

It should be easy to approximate the Hilbert transform using .

에서 주파수 응답이 널(null)이 발생하는 3형 선형위상 필터와는 달리

에서만 널이 발생하므로, 힐버트 변환 근사에 유리하다. 따라서 필터

의 차수

은 4형 선형위상 필터 구성이 가능하도록 홀수(odd) 임이 요구된다.On the other hand, in the case of a type 4 linear phase filter (Type 4), it is known that the same phase as the Hilbert transform is guaranteed,

Unlike the 3-type linear phase filter, where the frequency response is null,

Since null occurs only in , it is advantageous for the Hilbert transform approximation. So filter

degree of

is required to be odd so that a 4-type linear phase filter configuration is possible.

은 주파수 영역에서 주어진 임의의 위상 및 크기를 근사할 수 있어야 하므로, 필터의 설계를 위해 주파수 영역 최적화 기법의 적용이 요구된다. 주파수 영역 최적화 기법으로 최소제곱법이 알려져 있다. 주파수 영역 최소제곱법은 근사가 요구되는 주파수 대역에서만 최적화를 실시하므로, 근사 대역에서 정확도가 증대되는 장점이 있다. 다만, 주파수 영역 최소제곱 방법으로 근사 필터를 설계하는 것은 일 실시예이며, 공지의 다른 방법으로 필터를 설계할 수도 있다.Also filter

should be able to approximate any given phase and magnitude in the frequency domain, so it is required to apply the frequency domain optimization technique for the design of the filter. The least squares method is known as a frequency domain optimization technique. Since the frequency domain least-squares method optimizes only in the frequency band where approximation is required, there is an advantage in that the accuracy is increased in the approximation band. However, designing the approximate filter by the frequency domain least squares method is an embodiment, and the filter may be designed by other known methods.

라고 두고, 이를 근사하기 위한 필터

의 응답을

라고 하면, 근사대상 주파수 대역에서 가중 최소제곱 오차는 다음의 수학식 5와 같이 주어진다.The response of an ideal filter in the frequency domain least squares method is

, and a filter to approximate it

the response of

, the weighted least squares error in the approximate target frequency band is given by the following Equation (5).

(수학식 5)

(Equation 5)

: 오차가 정의된 근사대역,

: 0이상인 실수의 가중 함수)(only,

: the approximate band in which the error is defined,

: weighting function of real number greater than or equal to 0)

Equation 5 can be summarized as a quadratic expression such as Equation 6 below.

(수학식 6)

(Equation 6)

,

,

,

,

)(only,

,

,

,

,

)

는 복소 공액인 전치행렬(complex conjugate transpose)을 의미하고,

는 전치행렬을 의미하며,

는 복소공액을 의미한다. 수학식 6은 최적화 대상인 필터 계수의 이차식이므로, 그 구배를 0으로 두면 필터 계수를 다음의 수학식 7과 같이 얻는다.In Equation 6, the shoulder letter (superscript) is

means a complex conjugate transpose matrix,

is the transpose matrix,

is a complex conjugate. Since Equation 6 is a quadratic expression of the filter coefficient to be optimized, if the gradient is set to 0, the filter coefficient is obtained as in Equation 7 below.

(수학식 7)

(Equation 7)

으로 두었다. 진폭의 크기는 주파수와 무관하게 일정하며 위상만

로 일정하게 천이되는 상황에서,

및 차수가

일 때, 위의 방법으로 위상천이(phase shift) 필터를 설계한 결과는 도 4와 같다. 설계 결과 위상이

또는

인 경우, 필터가 정확한 위상을 가지는 것을 알 수 있으며, 다른 위상에서도 설계 대역인

내에서는 오차가 최소화됨을 확인할 수 있다.In order to confirm the design result of the filter, the ideal response assuming that the amplitude of the sound line is independent of the frequency

placed as The magnitude of the amplitude is constant independent of the frequency and only the phase

In a situation where there is a constant transition to

and degree

, the result of designing the phase shift filter in the above method is shown in FIG. 4 . As a result of the design

or

In the case of , it can be seen that the filter has the correct phase, and the design band is

It can be seen that the error is minimized in

에 이러한 손실이 반영되어야 한다. 이를 위해서 (수학식 5)에 따른 적분

및

를 수치적으로 계산하여야 한다. 수치 적분 방법으로는 알려진 trapzoidal rule 등의 1차원 적분 방법을 사용할 수 있다.In general, the magnitude and phase of the sound line amplitude are given as a function of frequency, such as volume loss and interface loss. Therefore, the ideal filter response

should reflect these losses. For this purpose, the integral according to (Equation 5)

and

should be calculated numerically. As the numerical integration method, a one-dimensional integration method such as a known trapzoidal rule may be used.

In an underwater environment, volume attenuation is known to increase with the length of the sound wave transmission path, and the ideal response reflecting this is the following Equation 8. Reflecting this, the characteristics of the filter designed through numerical integration are shown in FIG. 5 . In FIG. 5, the magnitude of the volume loss according to Equation 8 is indicated by a black dotted line, and it can be seen that the target volume loss is accurately reflected within the approximate band as a result of the filter design.

(수학식 8)

(Equation 8)

,

: 경로 길이

,

)(only,

,

: path length

,

)

는 신호를 해당 시간만큼 지연시켜 달성할 수 있다. 이 중 샘플 개수의 정수배에 해당하는 부분인

는 이산 시간에서 해당 샘플만큼 신호를 지연하는 것으로 해결이 되나, 남은 소수 시간지연(fractional delay)

는 이산시간 필터인

을 활용하여 근사적으로 처리되어야 한다. 특히 이러한 소수 시간지연이 적절히 반영되지 않으면, 상대적으로 작은 값을 가지는 배열 내의 센서간 시간지연 모의 정확도 저하로 인해, 빔형성 등의 신호처리 성능 검증 활용시 영향을 줄 수 있다.On the other hand, the arrival time delay of the intrinsic sound line given by Equation 3 is

can be achieved by delaying the signal by the corresponding amount of time. The part corresponding to an integer multiple of the number of samples

is solved by delaying the signal by the corresponding sample in discrete time, but the remaining fractional delay

is the discrete-time filter

should be approximated using In particular, if the fractional time delay is not properly reflected, the accuracy of time delay simulation between sensors in an array having a relatively small value decreases, which may affect the use of signal processing performance verification such as beamforming.

,

(샘플)라 하면, 주파수 대역에서 해당하는 위상을 가지는 이상적인 응답으로

을 얻는다. 설계필터

의 응답을

라고 하면, 주파수 영역 최소제곱 방법을 적용하기 위한 가중 최소제곱 오차는 수학식 5와 마찬가지로 다음의 수학식 9와 같이 주어진다.fractional time delay within the sample period

,

(Sample) is an ideal response having a corresponding phase in the frequency band.

get design filter

the response of

, the weighted least-squares error for applying the frequency domain least-squares method is given by the following Equation 9 as in Equation 5.

(수학식 9)

(Equation 9)

로 주어진 상황에서,

및 차수가

일 때, 위의 방법으로 소수 시간지연(fractional delay) 필터를 설계한 결과는 도 6과 같다. 분석 결과 근사 대역 내에서는 설계된 필터가 정확한 위상 시간지연을 가짐을 확인할 수 있다. 특히 도달 시간지연이

인 경우에는, 전체 대역에서 정확한 위상지연을 가진다. 한편 근사 대역 외의

영역에서는 오차가 발생하나, 주파수 중첩(aliasing) 문제로 인해 신호처리 시 해당 대역을 보통 활용하지 않으므로, 오차를 용인할 수 있다.To check the design result of the filter, a fractional time delay is

In the situation given by

and degree

, the result of designing a fractional delay filter by the above method is shown in FIG. 6 . As a result of the analysis, it can be confirmed that the designed filter has an accurate phase time delay within the approximate band. In particular, the arrival time delay

In the case of , it has an accurate phase delay in the entire band. On the other hand, out of the approximate band

Although an error occurs in the region, the corresponding band is not usually used in signal processing due to a frequency aliasing problem, so the error can be tolerated.

을 사용할 수 있다.Meanwhile, the phase delay of the filter designed in FIG. 6 is illustrated because there is interest in the time delay for each narrowband signal component within the approximate band. If the time delay of the envelope is important, such as a demodulation on noise (DEMON) signal, the design result of group delay can be reviewed instead of phase time delay. Given that, the ideal response is the same as above

can be used

Fig. 8 shows the results of deriving an underwater sound transmission channel (finite impulse response) from the natural sound line analysis results by applying the previously proposed discrete time simulation method. In the analysis of FIG. 8 , the water depth is 1000 m, the sound source depth is 10 m, and the receiver depth is 100 m, and the separation distance between the sound source and the receiver is 5 km. As environmental conditions, the sea level boundary was set as a vacuum, and the sea floor was set as an acoustic halfspace with a speed of sound of 1600 m/s and 1.8 times the unit density. Gaussian beam technique was applied as a sound line analysis method, 101 sound lines were used within ±12° of vertical angle, and volume loss was not reflected. For the sound velocity of the medium, the actual sound velocity profile measured in winter in the East Sea was applied. As a result of applying the proposed technique, it was confirmed that the discrete-time finite impulse response that can be used for computer simulation can be simulated from the results of natural sound analysis reflecting actual environmental conditions.

On the other hand, each step included in the method for simulating the underwater sound transmission channel according to the above-described embodiment may be implemented in a computer-readable recording medium for recording a computer program including instructions for performing these steps.

In addition, each step included in the method for simulating the hydroacoustic sound transmission channel according to the above-described embodiment is to be implemented in the form of a computer program stored in a computer-readable recording medium programmed to include instructions for performing these steps. can

As described so far, according to an embodiment of the present invention, a time-domain approximation and simulation method capable of minimizing an error based on a eigenline analysis technique capable of calculating the time delay of multiple paths in the time domain is provided. As such, by simulating an underwater sound wave transmission channel reflecting the underwater physical environment (sonic velocity profile, boundary surface topography and characteristics, etc.), it can be utilized in a simulator for sonar performance verification.

Combinations of each step in each flowchart attached to the present invention may be performed by computer program instructions. These computer program instructions may be embodied in a processor of a general purpose computer, special purpose computer, or other programmable data processing equipment, such that the instructions performed by the processor of the computer or other programmable data processing equipment provide the functions described in each step of the flowchart. It creates a means to do these things. These computer program instructions may also be stored in a computer-usable or computer-readable medium that may direct a computer or other programmable data processing equipment to implement a function in a particular manner, and thus the computer-usable or computer-readable medium. The instructions stored in the recording medium are also possible to produce an article of manufacture including instruction means for performing the functions described in each step of the flowchart. The computer program instructions may also be mounted on a computer or other programmable data processing equipment, such that a series of operational steps are performed on the computer or other programmable data processing equipment to create a computer-executed process to create a computer or other programmable data processing equipment. It is also possible that instructions for performing the processing equipment provide steps for performing the functions described in each step of the flowchart.

Further, each step may represent a module, segment, or portion of code comprising one or more executable instructions for executing the specified logical function(s). It should also be noted that in some alternative embodiments it is also possible for the functions recited in the steps to occur out of order. For example, it is possible that two steps shown one after another may in fact be performed substantially simultaneously, or that the steps may sometimes be performed in the reverse order depending on the function in question.

The above description is merely illustrative of the technical idea of the present invention, and various modifications and variations will be possible without departing from the essential quality of the present invention by those skilled in the art to which the present invention pertains. Accordingly, the embodiments disclosed in the present invention are not intended to limit the technical spirit of the present invention, but to explain, and the scope of the technical spirit of the present invention is not limited by these embodiments. The protection scope of the present invention should be interpreted by the following claims, and all technical ideas within the scope equivalent thereto should be interpreted as being included in the scope of the present invention.

Claims (11)

A method of simulating a hydroacoustic transmission channel by a hydroacoustic transmission channel simulation device, the method comprising:
deriving an eigenray solution for a plurality of eigenray paths between a sound source and a receiver;
Including the step of approximating the derived eigenline solution to a discrete time domain to derive a finite impulse response including information of an underwater acoustic transmission channel
A method of simulating a hydroacoustic transmission channel using a sound path. The method of claim 1,
The step of deriving the finite impulse response comprises:
designing an approximation filter for each eigenline capable of minimizing an error when approximating the eigenphone solution to the discrete time domain;
approximating the eigenphone solution using the eigenphone-specific approximation filter
A method of simulating a hydroacoustic transmission channel using a sound path. 3. The method of claim 2,
The eigenphone-by-tone approximation filter includes a phase and loss approximation filter and a fractional time delay approximation filter.
A method of simulating a hydroacoustic transmission channel using a sound path. 4. The method of claim 3,
The finite impulse response (g[n]) is expressed by the following equation

(only,

: sample index,

: number of distinct tones,

: convolution operation, round(): rounding operation,

: Phase and loss approximation filter of the i-th eigenline,

: Decimal time delay of the i-th unique tone (

, fractional delay) approximation filter,

filter order of ,

filter order of )
A method of simulating a hydroacoustic transmission channel using a sound path. 5. The method of claim 4,
The order of the phase and loss approximation filter is odd so that a 4-type linear phase filter configuration is possible.
A method of simulating an underwater acoustic transmission channel using a voice path. 5. The method of claim 4,
The phase and loss approximation filter is a frequency domain optimization technique applied
A method of simulating an underwater acoustic transmission channel using a voice path. 7. The method of claim 6,
As the frequency domain optimization technique, the frequency domain least squares method that optimizes only in the frequency band that requires approximation is applied.
A method of simulating an underwater acoustic transmission channel using a voice path. 8. The method of claim 7,
The response of the ideal filter in the frequency domain least squares method is

, and a filter to approximate it

the response of

, the weighted least-squares error in the approximate target frequency band is given by the following equation

(only,

: the approximate band in which the error is defined,

: weighting function of real number greater than or equal to 0)
A method of simulating an underwater acoustic transmission channel using a voice path. 5. The method of claim 4,
fractional time delay within the sample period

,

(Sample) is an ideal response having a corresponding phase in the frequency band.

, and the fractional time delay approximation filter

the response of

, the weighted least squares error for applying the frequency domain least squares method is given by the following equation

(However, [o, βπ]: approximate band with defined error,

: weighting function of real number greater than or equal to 0)
A method of simulating an underwater acoustic transmission channel using a voice path. As a computer-readable recording medium storing a computer program,
The computer program, when executed by a processor, includes the steps of deriving an eigenray solution for a plurality of eigenray paths between a sound source and a receiver, and approximating the derived eigenray solution to a discrete time domain for underwater acoustics A computer-readable recording medium comprising instructions for causing the processor to perform a hydroacoustic transmission channel simulation method including deriving a finite impulse response including information of the transmission channel. As a computer program stored in a computer-readable recording medium,
The computer program, when executed by a processor, includes the steps of deriving an eigenray solution for a plurality of eigenray paths between a sound source and a receiver, and approximating the derived eigenray solution to a discrete time domain for underwater acoustics A computer program comprising instructions for causing the processor to perform a hydroacoustic transmission channel simulation method comprising deriving a finite impulse response containing information of the transmission channel.

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