API Reference

_mean(x)::Real

Calculate the mean of a vector.

julia> using ArrayRadiation

julia> a = [1,2,3,4];

julia> ArrayRadiation.DspUtility._mean(a)
2.5

antenna_matrix(M, N, separation)

Generate locations (2D) for an evenly spaced MxN matrix of antenna elements, ensuring symmetry around the origin.

All elements are placed in the XY-plane.

Arguments

• M : Number of elements along the Y-axis.
• N : Number of elements along the X-axis.
• separation : Distance between adjacent elements.

Example

julia> using ArrayRadiation

julia> DspUtility.antenna_matrix(1, 2, 0.5)
1×2 Matrix{Tuple{Float64, Float64, Float64}}:
 (-0.25, 0.0, 0.0)  (0.25, 0.0, 0.0)

julia> DspUtility.antenna_matrix(1, 3, 1/2)
1×3 Matrix{Tuple{Float64, Float64, Float64}}:
 (-0.5, 0.0, 0.0)  (0.0, 0.0, 0.0)  (0.5, 0.0, 0.0)

julia> DspUtility.antenna_matrix(2, 1, 1/2)
2×1 Matrix{Tuple{Float64, Float64, Float64}}:
 (0.0, -0.25, 0.0)
 (0.0, 0.25, 0.0)

Convert between decibal scale (magnitude) and linear

Convert between decibal scale (power) and linear

discard_low_values(scalar_value::Real, lower_limit::Real)

This function takes a scalar value and compares it against a specified lower limit. If the scalar value is below the lower_limit, the function returns nothing. Otherwise, it returns the scalar value unchanged.

Arguments

• scalar_value::Real: The scalar value to compare.
• lower_limit::Real: The threshold value below which the scalar is discarded.

Example

julia> using ArrayRadiation

julia> ArrayRadiation.DspUtility.discard_low_values(50, 40)
50

julia> ArrayRadiation.DspUtility.discard_low_values(30, 40)

Return the signal energy in Joule

Generate locations (1D) for a evenly spaced array of N elements. N is even.

Arguments

• N Number of elements (assumed to be even).
• separation Distance between adjacent elements.

Convert between linear scale (magnitude) and decibel

Convert between linear scale (magnitude) and decibel

Return the average signal power in dBW

Return the average signal power in dBm

azimuth2k_hat(ϕ::Real)::Vector{Real}

Convert an azimuth angle ϕ (in radians) to a unit-length k-space vector in the XY-plane.

The resulting vector has the form [cos(ϕ), sin(ϕ), 0].

cos_taper_k_hat(k_hat_x::Real, k_hat_y::Real, α = 1.4)

Calculate cosine taper for normalized k-space vector [kx, ky, kz]/|k|.

Where |k| = 2π/λ0

Optionally provide α. α=1.4 accounts for mutual coupling between elements.

• R. A. Dana, Electronically Scanned Arrays and K-Space Gain Formulation, Springer, 2019.

elevation2k_hat(θ::Real)::Vector{Real}

Convert an elevation angle θ (in radians) to a unit-length k-space vector in the XZ-plane.

The resulting vector has the form [sin(θ), 0, cos(θ)].

gain(k_xyz::AbstractVector{<:Real}, Ge::Real, r_xyz::AbstractArray, element_weights::AbstractArray)

Calculate GΩ(k), the angular domain gain in direction k for an array with specified element weights.

Arguments

• k_xyz k-space vector.
• Ge The antena gain in direction k_xyz.
• r_xyz The placement of each antenna element. in
• element_weights The complex weight of each element. Must have the same size/shape as r_xyz.

References

• R. A. Dana, Electronically Scanned Arrays and K-Space Gain Formulation, Springer, 2019.

gain_1D(k_xyz::AbstractVector{<:Real}, Ge::Real, r_x::AbstractVector, element_weights::AbstractVector)

Calculate GΩ(k), the angular domain gain in direction k for an array with specified element weights.

Arguments

• k_xyz k-space vector.
• Ge The antena gain in direction k_xyz.
• r_x The placement of each antenna element. All elements are placed along the x-axis.
• element_weights The complex weight of each element.

References

• R. A. Dana, Electronically Scanned Arrays and K-Space Gain Formulation, Springer, 2019.

k2azimuth(k_xyz::Vector)::Real

Calculate the azimuth angle ϕ from a k-space vector.

The azimuth angle is the angle between the projection of the vector on the XY-plane and the x-axis.

k2elevation(k_xyz::Vector)::Real

Calculate the elevation angle θ from a k-space vector.

The elevation angle is the angle between the z unit vector and the the k vector.

k_xyz(θ::Real, ϕ::Real, λ0::Real=1)::Vector

Calculate k-space vector, representing antenna elevation and coordinates.

maximum_element_separation(max_look_angle_deg)

Calculate the maximum array element separation for maximum look angle.

Result is fraction of wavelenth.

cosine_q(M::Integer, q, scale = true)::AbstractVector

Create a coseine^q weighting (window).

Arguments

• M The length of the window.
• q For q=0 yields a uniform weight,q=1 yelds a cosine weighting, and q=2 yields a Hanning weighting.
• scale Max of window is 1, when not scaled. sum( cosine_q(M, q) ) = M when scaled.

Example

julia> using ArrayRadiation

julia> N = 64;

julia> W = Window.cosine_q(N, 1);

julia> round.( W[1:4], sigdigits=3 )
4-element Vector{Float64}:
 0.0385
 0.116
 0.192
 0.269

julia> round( sum(W), sigdigits=2)
64.0

References

• S. Yan, Broadband Array Processing, Springer, 2019

Returns 1:n but omits m.

split_window(W::AbstractVector)::AbstractVector

Split a window to create a difference beam

Arguments

• W The window to split.

Example

julia> using ArrayRadiation

julia> N = 64;

julia> W = Window.taylor(N, 4, -35);

julia> W = Window.split_window(W);

julia> round.( W[1:4], sigdigits=3 )
4-element Vector{Float64}:
 0.28
 0.288
 0.305
 0.329


julia> round.( W[N-3:N], sigdigits=3 )
4-element Vector{Float64}:
 -0.329
 -0.305
 -0.288
 -0.28

Below is an example of a split Taylor window.

taylor(N::Integer, n_bar::Integer, sll_dB::Real)::AbstractVector

Create taylor weighting (window).

Arguments

• N The window length.
• n_bar The number of nearly constant-level sidelobes adjacent to the main lobe.
• sll_dB Peak sidelobe_level in dB.

Example

julia> using ArrayRadiation

julia> W = Window.taylor(64, 4, -35);

julia> round.( W[1:4], sigdigits=3 )
4-element Vector{Float64}:
 0.28
 0.288
 0.305
 0.329

julia> round( sum(W), sigdigits=5)
64.0

References

• Carrar, Goodman and Majewski, Spotlight Synthetic Aperture Radar: Signal Processing Algorithms, Artech House, 1995

cardioid(θ::AbstractFloat, ϕ::AbstractFloat=0.0)

Calculate approximate radiation pattern for a cardioid antenna.

Arguments

• θ Elevation [rad]
• ϕ Azimuth [rad]

References

• Costa, Abrao, Rego, A Method for Approximating Directivity Expressions in Generalized Radiation Patterns, Elsevier, 2025.

cos_taper(θ::Real, α = 1.4)

Calculate cosine taper for elevation angle θ [rad]. Optionally provide α. α=1.4 accounts for mutual coupling between elements.

• R. A. Dana, Electronically Scanned Arrays and K-Space Gain Formulation, Springer, 2019.

half_wave_dipole(θ::AbstractFloat, ϕ::AbstractFloat=0.0)

Calculate approximate radiation pattern for a half wave dipole.

Arguments

• θ Elevation [rad]
• ϕ Azimuth [rad]

References

• Costa, Abrao, Rego, A Method for Approximating Directivity Expressions in Generalized Radiation Patterns, Elsevier, 2025.

microstrip_patch(θ::AbstractFloat, ϕ::AbstractFloat=0.0)

Calculate approximate radiation pattern for a microstrip patch antenna.

The model is only valid for θ ∈ [−π/2, π/2].

Arguments

• θ Elevation [rad]
• ϕ Azimuth [rad]

References

• Costa, Abrao, Rego, A Method for Approximating Directivity Expressions in Generalized Radiation Patterns, Elsevier, 2025.

yagi_uda(θ::AbstractFloat, ϕ::AbstractFloat=0.0)

Calculate approximate radiation pattern for a Yagi Uda antenna.

The model is only valid for θ ∈ [−π/2, π/2].

The model is based on the following geometry:

• Three directors, spaced 0.20λ apart.
• Director lengths: [0.428λ, 0.424λ, 0.428λ]
• Reflector length of 0.482λ

Arguments

• θ Elevation [rad]
• ϕ Azimuth [rad]

References

• Costa, Abrao, Rego, A Method for Approximating Directivity Expressions in Generalized Radiation Patterns, Elsevier, 2025.