Isotropic projector element
System object™ creates an isotropic sound projector used in 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 change the response using the
To compute the response of the isotropic projector for specified directions:
phased.IsotropicProjectorobject and set its properties.
Call the object with arguments, as if it were a function.
To learn more about how System objects work, see What Are System Objects?
creates an isotropic projector System object,
projector = phased.IsotropicProjector
creates an Isotropic projector object,
projector = phased.IsotropProjector(
projector, with each specified
property set to the specified value. You can specify additional name-value pair arguments
in any order as
projector = phased.IsotropicProjector(FrequencyRange=[0
1000],BackBaffled=true) creates an isotropic projector element with its
frequency range specified between 0 and 1000 Hz.
Unless otherwise indicated, properties are nontunable, which means you cannot change their
values after calling the object. Objects lock when you call them, and the
release function unlocks them.
If a property is tunable, you can change its value at any time.
For more information on changing property values, see System Design in MATLAB Using System Objects.
FrequencyRange — Operating frequency range of projector
[0 100e6] (default) | real-valued 1-by-2 vector
Operating frequency range of projector, specified as a 1-by-2 row vector in the form of
[LowerBound HigherBound]. This property defines the frequency range
over which the projector has a response. The projector element has zero response outside
this frequency range. Units are in Hz..
VoltageResponse — Voltage response of projector
120 (default) | scalar | real-valued 1-by-K row vector
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
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.
BackBaffled — Back baffle response of projector
false (default) |
Back baffle response of projector, specified as
true. Set this property to
true to back baffle
the projector response. When the projector is back baffled, 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
resp = projector(freq,ang)
The object performs an initialization the first time the object is executed. This
initialization locks nontunable properties
and input specifications, such as dimensions, complexity, and data type of the input data.
If you change a nontunable property or an input specification, the System object issues an error. To change nontunable properties or inputs, you must first
release method to unlock the object.
freq — Voltage response frequencies
positive real scalar | real-valued 1-by-L vector of positive values
Voltage response frequencies of projector, specified as a positive real scalar or a real-valued 1-by-L vector of positive values. Units are in Hz.
ang — Direction of arriving signals
real-valued 1-by-M row vector | real-valued 2-by-M matrix
Direction of arriving signals, specified as a real-valued
1-by-M row vector or 2-by-M matrix. When
ang is a 2-by-M matrix, each column of the
matrix specifies the direction in the form
azimuth angle must lie between –180° and 180°, inclusive. The elevation
angle must lie between –90° and 90°, inclusive.
ang is a 1-by-M row vector, each
element specifies the azimuth angle of the arriving signal. In this case, the
corresponding elevation angle is assumed to be zero.
resp — Voltage response of projector
real-valued M-by-L matrix
Voltage response of projector, returned as a real-valued
M-by-L matrix. M represents
the number of angles specified in
ang, and L
represents the number of frequencies specified in
freq. Units are
To use an object function, specify the
System object as the first input argument. For
example, to release system resources of a System object named
Specific to Antenna and Transducer Element System Objects
|Compute and display beamwidth of sensor element pattern|
|Directivity of antenna or transducer element|
|Antenna element polarization capability|
|Plot antenna or transducer element directivity and patterns|
|Plot antenna or transducer element directivity and pattern versus azimuth|
|Plot antenna or transducer element directivity and pattern versus elevation|
Response of Isotropic Projector
Find the response of an isotropic projector with default properties. Obtain the voltage response at five different elevation angles: -30°, -15°, 0°, 15° and 30°. All azimuth angles are set to 0°. The voltage response is computed at 2 kHz.
projector = phased.IsotropicProjector; fc = 2e3; resp = projector(fc,[0,0,0,0,0;-30,-15,0,15,30])
resp = 5×1 1 1 1 1 1
Response and Pattern of Isotropic Projector at Single Frequency
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', ... 'Type','power')
Plot Beamwidth of Isotropic Projector
Find the beamwidth of an isotropic underwater projector at 10 kHz.
First, create an isotropic projector element.
projector = phased.IsotropicProjector('FrequencyRange',[10 12000])
projector = phased.IsotropicProjector with properties: VoltageResponse: 120 FrequencyRange: [10 12000] BackBaffled: false
Then, use the beamwidth object function to plot the 3 dB beamwidth of the projector.
[bmw,angs] = beamwidth(projector,10000,'dbDown',3)
bmw = 360
angs = 1×2 -180 180
Because the projector is isotropic, there is no 3 dB down point.
Response and Pattern of Isotropic Projector at Multiple Frequencies
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
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', ... 'Type','power')
Directivity of Isotropic Projector
Compute the directivity of an isotropic projector in different directions. Assume the signal frequency is 3 kHz. First, set the projector parameters.
fc = 3e3; projector = phased.IsotropicProjector('FrequencyRange',[1,10]*1e3, ... 'VoltageResponse',[100,110,120,110,100]); patternElevation(projector,fc,45)
Select the angles of interest to be constant elevation angle at zero degrees. The five azimuth angles are centered around boresight (zero degrees azimuth and zero degrees elevation).
ang = [-20,-10,0,10,20; 0,0,0,0,0];
Compute the directivity along the constant elevation cut.
d = directivity(projector,fc,ang)
d = 5×1 0 0 0 0 0
The directivity of an isotropic projector is zero in every direction.
Azimuth Pattern of Isotropic Projector
Examine the azimuth pattern of an isotropic projector at 30° elevation. The frequency range is between 1 kHz and 10 kHz. Specify the voltage response as a scalar.
Set the projector parameters.
fc = 3e3; projector = phased.IsotropicProjector('FrequencyRange',[1,10]*1e3, ... 'VoltageResponse',-115); patternAzimuth(projector,fc,30)
Plot a smaller range of azimuth angles using the
Elevation Pattern of Isotropic Projector
Plot an elevation cut of the directivity of an isotropic projector at 45° azimuth. Assume the signal frequency is 3 kHz.
Create the isotropic projector object and call the pattern object function.
fc = 3e3; projector = phased.IsotropicProjector('FrequencyRange',[1,10]*1e3, ... 'VoltageResponse',70); patternElevation(projector,fc,45)
Plot a smaller range of elevation angles using the
Projector Voltage Response
The voltage response of a projector relates the transmitted sound intensity to the input voltage.
For a sound projector, the transmitting voltage response (TVR) is the sound intensity in µPa per volt, when measured at one meter from the projector. TVR is generally a function of frequency. If the sound intensity level (SIL) is expressed in dB//µPa and the output voltage (VdB) is expressed in dB//1V, then TVR is expressed in dB//µPa/1V. The output sound pressure level of a hydrophone is related to the input voltage level by
SIL = TVR + VdB.
SIL = TVR + VdB = 160 + 23 = 173 dB//µPa.
 Urick, R.J. Principles of Underwater Sound. 3rd Edition. New York: Peninsula Publishing, 1996.
 Sherman, C.S., and J. Butler. Transducers and Arrays for Underwater Sound. New York: Springer, 2007.
 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.
 Van Trees, H. Optimum Array Processing. New York: Wiley-Interscience, 2002, pp. 274–304.
C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.
Usage notes and limitations:
patternElevationmethods are not supported.
See System Objects in MATLAB Code Generation (MATLAB Coder).