phitheta2azelpat

Convert radiation pattern from phi-theta coordinates to azimuth-elevation coordinates

Syntax

pat_azel = phitheta2azelpat(pat_phitheta,phi,theta)

pat_azel = phitheta2azelpat(pat_phitheta,phi,theta,az,el)

pat_azel = phitheta2azelpat(___,'RotateZ2X',rotpatax)

[pat_azel,az_pat,el_pat]
= phitheta2azelpat(___)

Description

pat_azel = phitheta2azelpat(pat_phitheta,phi,theta) converts the antenna radiation pattern, pat_phitheta, from phi and theta coordinates to the pattern pat_azel in azimuth and elevation coordinates. phi and theta are the phi and theta coordinates at which pat_phitheta values are defined. The pat_azel matrix covers azimuth values from –180 to 180 degrees and elevation values from –90 to 90 degrees in one degree increments. The function interpolates the pat_phitheta matrix to estimate the response of the antenna in a given direction.

example

pat_azel = phitheta2azelpat(pat_phitheta,phi,theta,az,el) uses vectors az and el to specify the grid at which to sample pat_azel. To avoid interpolation errors, az should cover the range [–180, 180] and el should cover the range [–90, 90].

example

pat_azel = phitheta2azelpat(___,'RotateZ2X',rotpatax) also specifies rotpatax to indicate the boresight direction of the pattern: x-axis or z-axis.

example

[pat_azel,az_pat,el_pat] = phitheta2azelpat(___) also returns vectors az_pat and el_pat containing the azimuth and elevation angles at which pat_azel is sampled.

example

Examples

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Convert Radiation Pattern to Azimuth and Elevation

Open Live Script

Convert a radiation pattern to azimuth/elevation form, with the azimuth and elevation angles spaced 1° apart.

Define the pattern in terms of φ and θ.

phi = 0:360;
theta = 0:180;
pat_phitheta = mag2db(repmat(cosd(theta)',1,numel(phi)));

Convert the pattern to azimuth/elevation space.

pat_azel = phitheta2azelpat(pat_phitheta,phi,theta);

Plot Converted Radiation Pattern

Open Live Script

Convert a radiation pattern from theta/phi coordinates to azimuth/elevation coordinates, with azimuth and elevation angles spaced $1^{\circ}$ apart.

Define the pattern in terms of phi, $ϕ$ , and theta, $θ$ , coordinates.

phi = 0:360;
theta = 0:180;
pat_phitheta = mag2db(repmat(cosd(theta)',1,numel(phi)));

Convert the pattern to azimuth/elevation coordinates. Get the azimuth and elevation angles for use in plotting.

[pat_azel,az,el] = phitheta2azelpat(pat_phitheta,phi,theta);

Plot the radiation pattern.

H = surf(az,el,pat_azel);
H.LineStyle = 'none';
xlabel('Azimuth (degrees)');
ylabel('Elevation (degrees)');
zlabel('Pattern');

Figure contains an axes object. The axes object with xlabel Azimuth (degrees), ylabel Elevation (degrees) contains an object of type surface.

Convert Radiation Pattern from Alternate Phi-Theta Coordinates to Azimuth and Elevation

Open Live Script

Convert a radiation pattern to the azimuth-elevation coordinates from alternative phi-theta coordinates, with the phi and theta angles spaced one degree apart.

Create a simple radiation pattern in terms of phi and theta. Add an offset to the pattern to suppress taking the logarithm of zero in mag2db.

phi = 0:360;
theta = 0:180;
pat_phitheta = mag2db(10*sind(theta').^2*cosd(phi).^4 + 1);
imagesc(phi,theta,pat_phitheta)
xlabel('Phi (deg)')
ylabel('Theta (deg)')
colorbar

Figure contains an axes object. The axes object with xlabel Phi (deg), ylabel Theta (deg) contains an object of type image.

[pat_azel,az_pat,el_pat] = phitheta2azelpat(pat_phitheta,phi,theta,'RotateZ2X',false);
imagesc(az_pat,el_pat,pat_azel)
xlabel('Azimuth (deg)')
ylabel('Elevation (deg)')
colorbar

Figure contains an axes object. The axes object with xlabel Azimuth (deg), ylabel Elevation (deg) contains an object of type image.

Convert Radiation Pattern for Specific Azimuth/Elevation Values

Open Live Script

Convert a radiation pattern from phi/theta coordinates to azimuth/elevation coordinates, with the azimuth and elevation angles spaced $5^{\circ}$ apart.

Define the pattern in terms of phi and theta.

phi = 0:360;
theta = 0:180;
pat_phitheta = mag2db(repmat(cosd(theta)',1,numel(phi)));

Define the set of azimuth and elevation angles at which to sample the pattern. Then, convert the pattern.

az = -180:5:180;
el = -90:5:90;
pat_azel = phitheta2azelpat(pat_phitheta,phi,theta,az,el);

Plot the radiation pattern.

H = surf(az,el,pat_azel);
H.LineStyle = 'none';
xlabel('Azimuth (degrees)');
ylabel('Elevation (degrees)');
zlabel('Pattern');

Figure contains an axes object. The axes object with xlabel Azimuth (degrees), ylabel Elevation (degrees) contains an object of type surface.

Input Arguments

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`pat_phitheta` — Antenna radiation patter
real-valued Q-by-P matrix

Antenna radiation pattern in phi-theta coordinates, specified as a real-valued Q-by-P matrix. pat_phitheta contains the magnitude pattern. P is the length of the phi vector, and Q is the length of the theta vector. Units are in dB.

Data Types: double

`phi` — Phi angles
real-valued length-P vector

Phi angles at which pat_phitheta is sampled, specified as a vector of real-valued length-P vector. Phi angles lie between 0 and 360, inclusive. Units are in degrees.

Data Types: double

`theta` — Theta angles
real-valued length-Q vector

Theta angles at which pat_phitheta is sampled, specified as a vector of real-valued length-Q vector. Theta angles lie between 0 and 180, inclusive. Units are in degrees.

Data Types: double

`az` — Azimuth angles
`[-180:180]` (default) | real-valued length-L vector

Azimuth angles at which pat_azel samples the pattern, specified as a vector of real-valued length-L vector. Azimuth angles lie between –180 and 180, inclusive. Units are in degrees.

Data Types: double

`el` — Elevation angles
`[-90:90]` (default) | real-valued length-M vector

Elevation angles at which pat_azel samples the pattern, specified as a real-valued length-M vector. Elevation angle lie between –90 and 90, inclusive. Units are in degrees.

Data Types: double

`rotpatax` — Pattern boresight direction selector
`true` (default) | `false`

Pattern boresight direction selector, specified as true or false.

If rotpatax is true, the pattern boresight is along the x-axis. In this case, the z-axis of phi-theta space is aligned with the x-axis of azimuth and elevation space. The phi angle is defined from the y-axis to the z-axis and the theta angle is defined from the x-axis toward the yz-plane. (See Phi and Theta Angles).
If rotpatax is false, the phi angle is defined from the x-axis to the y-axis and the theta angle is defined from the z-axis toward the xy-plane. (See Alternative Definition of Phi and Theta).

Data Types: logical

Output Arguments

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`pat_azel` — Antenna radiation pattern in azimuth-elevation coordinates
real-valued M-by-L matrix

Antenna radiation pattern in azimuth-elevation coordinates, returned as a real-valued M-by-L matrix. pat_azel represents the magnitude pattern. L is the length of the az_pat vector, and M is the length of the el_pat vector. Units are in dB.

`az_pat` — Azimuth angles
real-valued length-L vector

Azimuth angles at which the pat_azel output pattern is sampled, returned as a real-valued length-L vector. Units are in degrees.

`el_pat` — Elevation angles
real-valued length-M vector

Elevation angles at which the pat_azel output pattern is sampled, returned as a real-valued length-M vector. Units are in degrees.

More About

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Azimuth and Elevation Angles

The azimuth angle of a vector is the angle between the x-axis and the orthogonal projection of the vector onto the xy plane. The angle is positive in going from the x axis toward the y axis. Azimuth angles lie between –180 and 180 degrees. The elevation angle is the angle between the vector and its orthogonal projection onto the xy-plane. The angle is positive when going toward the positive z-axis from the xy plane. By default, the boresight direction of an element or array is aligned with the positive x-axis. The boresight direction is the direction of the main lobe of an element or array.

Note

The elevation angle is sometimes defined in the literature as the angle a vector makes with the positive z-axis. The MATLAB^® and Phased Array System Toolbox™ products do not use this definition.

This figure illustrates the azimuth angle and elevation angle for a vector shown as a green solid line.

Phi and Theta Angles

The phi angle (φ) is the angle from the positive y-axis to the vector’s orthogonal projection onto the yz plane. The angle is positive toward the positive z-axis. The phi angle is between 0 and 360 degrees. The theta angle (θ) is the angle from the x-axis to the vector itself. The angle is positive toward the yz plane. The theta angle is between 0 and 180 degrees.

The figure illustrates phi and theta for a vector that appears as a green solid line.

The coordinate transformations between φ/θ and az/el are described by the following equations

$\begin{array}{l} \sin e l = \sin ϕ \sin θ \\ \tan a z = \cos ϕ \tan θ \\ \cos θ = \cos e l \cos a z \\ \tan ϕ = \tan e l / \sin a z \end{array}$

Alternative Definition of Phi and Theta

The phi angle (φ) is the angle from the positive x-axis to the vector’s orthogonal projection onto the xy plane. The angle is positive toward the positive y-axis. The phi angle is between 0 and 360 degrees. The theta angle (θ) is the angle from the z-axis to the vector itself. The angle is positive toward the xy plane. The theta angle is between 0 and 180 degrees.

The figure illustrates φ and θ for a vector that appears as a green solid line.

$\begin{array}{l} ϕ = a z \\ θ = 90 - e l \\ a z = ϕ \\ e l = 90 - θ \end{array}$

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.

Usage notes and limitations:

Does not support variable-size inputs.

Version History

Introduced in R2012a

phitheta2azelpat

Syntax

Description

Examples

Convert Radiation Pattern to Azimuth and Elevation

Plot Converted Radiation Pattern

Convert Radiation Pattern from Alternate Phi-Theta Coordinates to Azimuth and Elevation

Convert Radiation Pattern for Specific Azimuth/Elevation Values

Input Arguments

`pat_phitheta` — Antenna radiation patter
real-valued Q-by-P matrix

`phi` — Phi angles
real-valued length-P vector

`theta` — Theta angles
real-valued length-Q vector

`az` — Azimuth angles
`[-180:180]` (default) | real-valued length-L vector

`el` — Elevation angles
`[-90:90]` (default) | real-valued length-M vector

`rotpatax` — Pattern boresight direction selector
`true` (default) | `false`

Output Arguments

`pat_azel` — Antenna radiation pattern in azimuth-elevation coordinates
real-valued M-by-L matrix

`az_pat` — Azimuth angles
real-valued length-L vector

`el_pat` — Elevation angles
real-valued length-M vector

More About

Azimuth and Elevation Angles

Phi and Theta Angles

Alternative Definition of Phi and Theta

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.

Version History

See Also

Topics

phitheta2azelpat

Syntax

Description

Examples

Convert Radiation Pattern to Azimuth and Elevation

Plot Converted Radiation Pattern

Convert Radiation Pattern from Alternate Phi-Theta Coordinates to Azimuth and Elevation

Convert Radiation Pattern for Specific Azimuth/Elevation Values

Input Arguments

pat_phitheta — Antenna radiation patter real-valued Q-by-P matrix

phi — Phi angles real-valued length-P vector

theta — Theta angles real-valued length-Q vector

az — Azimuth angles [-180:180] (default) | real-valued length-L vector

el — Elevation angles [-90:90] (default) | real-valued length-M vector

rotpatax — Pattern boresight direction selector true (default) | false

Output Arguments

pat_azel — Antenna radiation pattern in azimuth-elevation coordinates real-valued M-by-L matrix

az_pat — Azimuth angles real-valued length-L vector

el_pat — Elevation angles real-valued length-M vector

More About

Azimuth and Elevation Angles

Phi and Theta Angles

Alternative Definition of Phi and Theta

Extended Capabilities

C/C++ Code Generation Generate C and C++ code using MATLAB® Coder™.

Version History

See Also

Topics

`pat_phitheta` — Antenna radiation patter
real-valued Q-by-P matrix

`phi` — Phi angles
real-valued length-P vector

`theta` — Theta angles
real-valued length-Q vector

`az` — Azimuth angles
`[-180:180]` (default) | real-valued length-L vector

`el` — Elevation angles
`[-90:90]` (default) | real-valued length-M vector

`rotpatax` — Pattern boresight direction selector
`true` (default) | `false`

`pat_azel` — Antenna radiation pattern in azimuth-elevation coordinates
real-valued M-by-L matrix

`az_pat` — Azimuth angles
real-valued length-L vector

`el_pat` — Elevation angles
real-valued length-M vector

C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.