# tsSignature

Target strength pattern

## Description

tsSignature creates a sonar target strength (TS) signature object. You can use this object to model an angle-dependent and frequency-dependent target strength pattern. Target strength determines the intensity of reflected sound signal power from a target.

## Creation

### Description

tssig = tsSignature creates a tsSignature object with default property values.

example

tssig = tsSignature(Name,Value) sets object properties using one or more Name,Value pair arguments. Name is a property name and Value is the corresponding value. Name must appear inside single quotes (''). You can specify several name-value pair arguments in any order as Name1,Value1,...,NameN,ValueN. Any unspecified properties take default values.

Note

You can only set property values of tsSignature when constructing the object. The property values are not changeable after construction.

## Properties

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Sampled target strength pattern, specified as a scalar, a Q-by-P real-valued matrix, or a Q-by-P-by-K real-valued array. The pattern is an array of TS values defined on a grid of elevation angles, azimuth angles, and frequencies. Azimuth and elevation are defined in the body frame of the target.

• Q is the number of TS samples in elevation.

• P is the number of TS samples in azimuth.

• K is the number of TS samples in frequency.

Q, P, and K usually match the length of the vectors defined in the Elevation, Azimuth, and Frequency properties, respectively, with these exceptions:

• To model a TS pattern for an elevation cut (constant azimuth), you can specify the TS pattern as a Q-by-1 vector or a 1-by-Q-by-K matrix. Then, the elevation vector specified in the Elevation property must have length 2.

• To model a TS pattern for an azimuth cut (constant elevation), you can specify the TS pattern as a 1-by-P vector or a 1-by-P-by-K matrix. Then, the azimuth vector specified in the Azimuth property must have length 2.

• To model a TS pattern for one frequency, you can specify the TS pattern as a Q-by-P matrix. Then, the frequency vector specified in the Frequency property must have length 2.

Example: [10,0;0,-5]

Data Types: double

Azimuth angles used to define the angular coordinates of each column of the matrix or array specified by the Pattern property. Specify the azimuth angles as a length-P vector. P must be greater than two. Angle units are in degrees.

Example: [-45:0.1:45]

Data Types: double

Elevation angles used to define the coordinates of each row of the matrix or array specified by the Pattern property. Specify the elevation angles as a length-Q vector. Q must be greater than two. Angle units are in degrees.

Example: [-30:0.1:30]

Data Types: double

Frequencies used to define the applicable target strength for each page of the Pattern property, specified as a K-element vector of positive scalars. K is the number of TS samples in frequency. K must be no less than two. Frequency units are in hertz.

Example: [0:0.1:30]

Data Types: double

## Object Functions

 value Target strength at specified angle and frequency toStruct Convert to structure

## Examples

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Specify the target strength (TS) of a 5m long rigid cylinder immersed in water and plot TS values along an azimuth cut. Assume the short-wavelength approximation. The cylinder radius is 2m. The speed of sound is 1520 m/s.

L = 5;
a = 2;

Create an array of target strengths at two wavelengths. First, specify the range of azimuth and elevation angles over which TS is defined. Then, use an analytical model to compute the target strength. Create an image of the TS.

lambda = [0.12, .1];
c = 1520.0;
az = [-20:0.1:20];
el = [-10:0.1:10];
ts1 = ts_cylinder(L,a,az,el,lambda(1));
ts2 = ts_cylinder(L,a,az,el,lambda(2));
tsdb1 = 10*log10(ts1);
tsdb2 = 10*log10(ts2);
imagesc(az,el,tsdb1)
title('Target Strength')
xlabel('Azimuth (deg)')
ylabel('Elevation (deg)')
colorbar

Create a tsSignature object and plot an elevation cut at $3{0}^{\circ }$ azimuth.

tsdb(:,:,1) = tsdb1;
tsdb(:,:,2) = tsdb2;
freq = c./lambda;
tssig = tsSignature('Pattern',tsdb,'Azimuth',az,'Elevation',el,'Frequency',freq);
ts = value(tssig,30,el,freq(1));
plot(el,tsdb1)
grid
title('Elevation Profile of Target Strength')
xlabel('Elevation (deg)')
ylabel('TS (dBsm)')

function ts = ts_cylinder(L,a,az,el,lambda)
k = 2*pi/lambda;
beta = k*L*sind(el')*ones(size(az));
gamma = cosd(el')*ones(size(az));
ts = a*L^2*(sinc(beta).^2).*gamma.^2/2/lambda;
ts = max(ts,10^(-5));
end

function s = sinc(theta)
s = ones(size(theta));
idx = (abs(theta) <= 1e-2);
s(idx) = 1 - 1/6*(theta(idx)).^2;
s(~idx) = sin(theta(~idx))./theta(~idx);
end

## References

[1] Urich, Robert J. Principles of Underwater Sound, 3rd ed. New York: McGraw-Hill, Inc. 2005.

## Version History

Introduced in R2018b