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Isotropic projector


The phased.IsotropicProjector System object™ creates an isotropic sound projector for sonar applications. An isotropic projector has the same response in all directions. The response is the radiated sound intensity per unit input voltage to the projector. You can adjust the response using the VoltageResponse property.

To compute the response of a projector for specified directions:

  1. Define and set up an isotropic projector System object. See Construction.

  2. Call step to compute the response according to the properties of phased.IsotropicProjector.


Instead of using the step method to perform the operation defined by the System object, you can call the object with arguments, as if it were a function. For example, y = step(obj,x) and y = obj(x) perform equivalent operations.


projector = phased.IsotropicProjector creates an isotropic projector System object, projector.

projector = phased.IsotropicProjector(Name,Value) creates an isotropic projector System object, projector, with each specified property Name set to the specified Value. You can specify additional name-value pair arguments in any order as (Name1,Value1,...,NameN,ValueN).


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Operating frequency range of projector, specified as a 1-by-2 row vector in the form of [LowerBound HigherBound]. The projector defines the nonzero response range over which the hydrophone has a response. The projector has zero response outside this frequency range. Units are Hz.

Example: [0 10e3]

Data Types: double

Voltage response of projector, specified as a scalar or real-valued 1-by-K row vector. When you specify voltage response as a scalar, that value applies to the entire frequency range specified by FrequencyRange. When you specify the voltage sensitivity as a vector, the frequency range is divided into K-1 equal intervals. The response values are assigned to the interval end points. Then, the step method interpolates the voltage response for any frequency inside the frequency range. Units are in dB ref: 1 μPa/V. See Projector Voltage Response for more details.

Example: 10

Data Types: double

Backbaffle response of projector, specified as false or true. Set this property to true to backbaffle the projector response. When the projector is backbaffled, the projector response for all azimuth angles beyond ±90° from broadside are zero. Broadside is defined as 0° azimuth and 0° elevation.

When the value of this property is false, the projector is not backbaffled.


Specific to phased.IsotropicProjector Object

Compute and display beamwidth of sensor element pattern


Directivity of isotropic projector


Polarization capability


Plot isotropic projector directivity and patterns


Plot isotropic projector directivity and response patterns versus azimuth


Plot isotropic projector directivity and response patterns versus elevation


Voltage sensitivity of isotropic projector

Common to All System Objects

Allow System object property value changes


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Examine the response and patterns of an isotropic projector operating between 1 kHz and 10 kHz.

Set the projector parameters and obtain the voltage response at five different elevation angles: -30°, -15°, 0°, 15° and 30°. All elevation angles at 0° azimuth angle. The voltage response is computed at 2 kHz.

projector = phased.IsotropicProjector('FrequencyRange',[1,10]*1e3);
fc = 2e3;
resp = projector(fc,[0,0,0,0,0;-30,-15,0,15,30]);

Draw a 3-D plot of the voltage response.

pattern(projector,fc,[-180:180],[-90:90],'CoordinateSystem','polar', ...

Examine the response and patterns of an isotropic projector at three different frequencies. The projector operates between 1 kHz and 10 kHz. Specify the voltage response as a vector.

Set up the projector parameters, and obtain the voltage response at 45° azimuth and 30° elevation. Compute the responses at signal frequencies of 2, 5, and 7 kHz.

projector = phased.IsotropicProjector('FrequencyRange',[1 10]*1e3, ...
    'VoltageResponse',[90 95 100 95 90]);
fc = [2e3 5e3 7e3];
resp = projector(fc,[45;30]);
resp = 1×3

    0.0426    0.0903    0.0708

Next, draw a 2-D plot of the voltage response as a function of azimuth.

pattern(projector,fc,[-180:180],0,'CoordinateSystem','rectangular', ...

Figure contains an axes object. The axes object with title Azimuth Cut (elevation angle = 0.0°) contains 3 objects of type line. These objects represent 2 kHz, 5 kHz, 7 kHz.

More About

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[1] Urick, R.J. Principles of Underwater Sound. 3rd Edition. New York: Peninsula Publishing, 1996.

[2] Sherman, C.S., and J. Butler. Transducers and Arrays for Underwater Sound. New York: Springer, 2007.

[3] Allen, J.B., and D. Berkely. “Image method for efficiently simulating small-room acoustics”, Journal of the Acoustical Society of America. Vol. 65, No. 4. April 1979, , pp. 943–950.

[4] Van Trees, H. Optimum Array Processing. New York: Wiley-Interscience, 2002, pp. 274–304.

Extended Capabilities

Introduced in R2017a