Array signal processing

Frequency-domain Bartlett beamformer.

Frequency-domain Capon beamformer with diagonal loading factor γ.

Frequency-domain MUSIC beamformer with nsignals signals.

beamform(s, f, n, sd; fs=framerate(s), method=Bartlett())
beamform(s, f, sd; fs=framerate(s), method=Bartlett())

Narrowband frequency-domain beamformer. Takes in passband signals s and produces beamformer output for all directions specified by the steering delays sd. The beamformer output is an energy estimate (or equivalent) for each steering direction. The beamforming only uses a narrowband signal cenetered at frequency f with a bandwidth of about fs/n.

If n is not specified, or is 1, then the input signal is assumed to be narrowband, and centered at frequency f.

The narrowband assumption requires that the bandwidth be no greater than about 5/T, where T is the maximum time taken for a signal to propagate through the array.

Several beamforming methods are available:

• Bartlett()
• Capon(γ)
• Music(nsignals)

Custom beamformers can be implemented by creating a subtype of SignalAnalysis.Beamformer and implementing the SignalAnalysis.beamformer() method dispatched on that type.

Example:

julia> x = cw(100.0, 1.0, 44100.0);
julia> sd = steering(0.0:1.0:3.0, 1500.0, range(0.0, π; length=181));
julia> bfo = beamform([x x x x], 100.0, 4096, sd; method=Capon(0.1))
181-element Array{Float64,1}:
 0.12406290296318974
 0.1240975045516605
 ⋮
 0.12406290296318974

beamform(s, sd; fs=framerate(s))

Broadband time-domain delay-and-sum beamformer. Takes in passband or baseband signals s and produces beamformer output for all directions specified by the steering delays sd. The beamformer output is a timeseries signal for each steering direction.

Example:

julia> x = cw(100.0, 1.0, 44100.0);
julia> sd = steering(0.0:1.0:3.0, 1500.0, range(0.0, π; length=181));
julia> bfo = beamform([x x x x], sd)
44100-frame, 181-channel SampleBuf{Complex{Float64}, 2}
1.0s sampled at 44100.0Hz
  ⋮

steering(rxpos, c, θ)

Computes steering delays for specified receiver positions rxpos, signal propagation speed c, and angles θ. The delays are computed with a far-field assumption, i.e., for plane incoming waves.

Examples:

julia> steering(0.0:1.0:5.0, 1500.0, range(0.0, π; length=181))
6×181 Array{Float64,2}:
  0.00166667    0.00166641   …  -0.00166641   -0.00166667
  0.001         0.000999848     -0.000999848  -0.001
  0.000333333   0.000333283     -0.000333283  -0.000333333
 -0.000333333  -0.000333283      0.000333283   0.000333333
 -0.001        -0.000999848      0.000999848   0.001
 -0.00166667   -0.00166641   …   0.00166641    0.00166667

julia> rxpos = [  # can be 2D or 3D coordinates
  0.0  1.0  2.0  3.0  4.0  5.0
  0.0  0.0  0.0  0.0  0.0  0.0
];
julia> steering(rxpos, 1500.0, range(0.0, π; length=181))
6×181 Array{Float64,2}:
  0.00166667    0.00166641   …  -0.00166641   -0.00166667
  0.001         0.000999848     -0.000999848  -0.001
  0.000333333   0.000333283     -0.000333283  -0.000333333
 -0.000333333  -0.000333283      0.000333283   0.000333333
 -0.001        -0.000999848      0.000999848   0.001
 -0.00166667   -0.00166641   …   0.00166641    0.00166667