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| <html lang="en"><head><meta charset="UTF-8"/><meta name="viewport" content="width=device-width, initial-scale=1.0"/><title>Array signal processing · SignalAnalysis.jl</title><script data-outdated-warner src="assets/warner.js"></script><link href="https://cdnjs.cloudflare.com/ajax/libs/lato-font/3.0.0/css/lato-font.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/juliamono/0.045/juliamono.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.15.4/css/fontawesome.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.15.4/css/solid.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.15.4/css/brands.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.13.24/katex.min.css" rel="stylesheet" type="text/css"/><script>documenterBaseURL="."</script><script src="https://cdnjs.cloudflare.com/ajax/libs/require.js/2.3.6/require.min.js" data-main="assets/documenter.js"></script><script src="siteinfo.js"></script><script src="../versions.js"></script><link class="docs-theme-link" rel="stylesheet" type="text/css" href="assets/themes/documenter-dark.css" data-theme-name="documenter-dark" data-theme-primary-dark/><link class="docs-theme-link" rel="stylesheet" type="text/css" href="assets/themes/documenter-light.css" data-theme-name="documenter-light" data-theme-primary/><script src="assets/themeswap.js"></script></head><body><div id="documenter"><nav class="docs-sidebar"><div class="docs-package-name"><span class="docs-autofit"><a href="index.html">SignalAnalysis.jl</a></span></div><form class="docs-search" action="search.html"><input class="docs-search-query" id="documenter-search-query" name="q" type="text" placeholder="Search docs"/></form><ul class="docs-menu"><li><a class="tocitem" href="index.html">Home</a></li><li><span class="tocitem">Manual</span><ul><li><a class="tocitem" href="signals.html">Creating & managing signals</a></li><li><a class="tocitem" href="generate.html">Generating signals</a></li><li><a class="tocitem" href="basic.html">Basic signal analysis</a></li><li><a class="tocitem" href="dsp.html">Signal processing</a></li><li><a class="tocitem" href="tfa.html">Time-frequency analysis</a></li><li class="is-active"><a class="tocitem" href="array.html">Array signal processing</a></li><li><a class="tocitem" href="rand.html">Random noise generation</a></li><li><a class="tocitem" href="plot.html">Plot recipes</a></li></ul></li></ul><div class="docs-version-selector field has-addons"><div class="control"><span class="docs-label button is-static is-size-7">Version</span></div><div class="docs-selector control is-expanded"><div class="select is-fullwidth is-size-7"><select id="documenter-version-selector"></select></div></div></div></nav><div class="docs-main"><header class="docs-navbar"><nav class="breadcrumb"><ul class="is-hidden-mobile"><li><a class="is-disabled">Manual</a></li><li class="is-active"><a href="array.html">Array signal processing</a></li></ul><ul class="is-hidden-tablet"><li class="is-active"><a href="array.html">Array signal processing</a></li></ul></nav><div class="docs-right"><a class="docs-edit-link" href="https://github.com/org-arl/SignalAnalysis.jl/blob/master/docs/src/array.md" title="Edit on GitHub"><span class="docs-icon fab"></span><span class="docs-label is-hidden-touch">Edit on GitHub</span></a><a class="docs-settings-button fas fa-cog" id="documenter-settings-button" href="#" title="Settings"></a><a class="docs-sidebar-button fa fa-bars is-hidden-desktop" id="documenter-sidebar-button" href="#"></a></div></header><article class="content" id="documenter-page"><h1 id="Array-signal-processing"><a class="docs-heading-anchor" href="#Array-signal-processing">Array signal processing</a><a id="Array-signal-processing-1"></a><a class="docs-heading-anchor-permalink" href="#Array-signal-processing" title="Permalink"></a></h1><article class="docstring"><header><a class="docstring-binding" id="SignalAnalysis.Bartlett" href="#SignalAnalysis.Bartlett"><code>SignalAnalysis.Bartlett</code></a> — <span class="docstring-category">Type</span></header><section><div><p>Frequency-domain Bartlett beamformer.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/org-arl/SignalAnalysis.jl/blob/fa182dd4c6d63f73d06de96ca6f106cff83d006c/src/array.jl#L9-L11">source</a></section></article><article class="docstring"><header><a class="docstring-binding" id="SignalAnalysis.Capon" href="#SignalAnalysis.Capon"><code>SignalAnalysis.Capon</code></a> — <span class="docstring-category">Type</span></header><section><div><p>Frequency-domain Capon beamformer with diagonal loading factor <code>γ</code>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/org-arl/SignalAnalysis.jl/blob/fa182dd4c6d63f73d06de96ca6f106cff83d006c/src/array.jl#L14-L16">source</a></section></article><article class="docstring"><header><a class="docstring-binding" id="SignalAnalysis.Music" href="#SignalAnalysis.Music"><code>SignalAnalysis.Music</code></a> — <span class="docstring-category">Type</span></header><section><div><p>Frequency-domain MUSIC beamformer with <code>nsignals</code> signals.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/org-arl/SignalAnalysis.jl/blob/fa182dd4c6d63f73d06de96ca6f106cff83d006c/src/array.jl#L21-L23">source</a></section></article><article class="docstring"><header><a class="docstring-binding" id="SignalAnalysis.beamform-NTuple{4, Any}" href="#SignalAnalysis.beamform-NTuple{4, Any}"><code>SignalAnalysis.beamform</code></a> — <span class="docstring-category">Method</span></header><section><div><pre><code class="language-julia hljs">beamform(s, f, n, sd; fs=framerate(s), method=Bartlett()) | ||
| beamform(s, f, sd; fs=framerate(s), method=Bartlett())</code></pre><p>Narrowband frequency-domain beamformer. Takes in passband signals <code>s</code> and produces beamformer output for all directions specified by the steering delays <code>sd</code>. The beamformer output is an energy estimate (or equivalent) for each steering direction. The beamforming only uses a narrowband signal cenetered at frequency <code>f</code> with a bandwidth of about <code>fs/n</code>.</p><p>If <code>n</code> is not specified, or is 1, then the input signal is assumed to be narrowband, and centered at frequency <code>f</code>.</p><p>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.</p><p>Several beamforming methods are available:</p><ul><li><a href="array.html#SignalAnalysis.Bartlett"><code>Bartlett</code></a><code>()</code></li><li><a href="array.html#SignalAnalysis.Capon"><code>Capon</code></a><code>(γ)</code></li><li><a href="array.html#SignalAnalysis.Music"><code>Music</code></a><code>(nsignals)</code></li></ul><p>Custom beamformers can be implemented by creating a subtype of <code>SignalAnalysis.Beamformer</code> and implementing the <code>SignalAnalysis.beamformer()</code> method dispatched on that type.</p><p><strong>Example:</strong></p><pre><code class="language-julia-repl hljs">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</code></pre></div><a class="docs-sourcelink" target="_blank" href="https://github.com/org-arl/SignalAnalysis.jl/blob/fa182dd4c6d63f73d06de96ca6f106cff83d006c/src/array.jl#L137-L174">source</a></section></article><article class="docstring"><header><a class="docstring-binding" id="SignalAnalysis.beamform-Tuple{Any, Any}" href="#SignalAnalysis.beamform-Tuple{Any, Any}"><code>SignalAnalysis.beamform</code></a> — <span class="docstring-category">Method</span></header><section><div><pre><code class="language-julia hljs">beamform(s, sd; fs=framerate(s))</code></pre><p>Broadband time-domain delay-and-sum beamformer. Takes in passband or baseband signals <code>s</code> and produces beamformer output for all directions specified by the steering delays <code>sd</code>. The beamformer output is a timeseries signal for each steering direction.</p><p><strong>Example:</strong></p><pre><code class="language-julia-repl hljs">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) | ||
| SampledSignal @ 44100.0 Hz, 44100×181 Array{Complex{Float64},2}: | ||
| ⋮</code></pre></div><a class="docs-sourcelink" target="_blank" href="https://github.com/org-arl/SignalAnalysis.jl/blob/fa182dd4c6d63f73d06de96ca6f106cff83d006c/src/array.jl#L109-L125">source</a></section></article><article class="docstring"><header><a class="docstring-binding" id="SignalAnalysis.steering-Tuple{AbstractMatrix{T} where T, Any, AbstractVector{T} where T}" href="#SignalAnalysis.steering-Tuple{AbstractMatrix{T} where T, Any, AbstractVector{T} where T}"><code>SignalAnalysis.steering</code></a> — <span class="docstring-category">Method</span></header><section><div><pre><code class="language-julia hljs">steering(rxpos, c, θ) | ||
| </code></pre><p>Computes steering delays for specified receiver positions <code>rxpos</code>, signal propagation speed <code>c</code>, and angles <code>θ</code>. Array <code>θ</code> can be a 1D array of angles or 2D array with (azimuth, elevation) pair in each row. The delays are computed with a far-field assumption, i.e., for plane incoming waves.</p><p><strong>Examples:</strong></p><pre><code class="language-julia-repl hljs">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 | ||
|
|
||
| julia> rxpos = [ | ||
| 0.0 0.0 0.5 0.5 | ||
| 0.0 0.5 0.0 0.5 | ||
| 0.0 0.0 0.0 0.0 | ||
| ]; | ||
| julia> θ = deg2rad.(reduce(vcat, hcat.(LinRange(-20,20,41)', LinRange(-10,10,21)))) # 2D array with (azimuth, elevation) in each row | ||
| julia> steering(rxpos, 1500.0, θ) | ||
| 4×861 Array{Float64,2}: | ||
| 9.80987e-5 9.83857e-5 9.86427e-5 … 0.00021154 0.000210989 0.000210373 | ||
| 0.000210373 0.000210989 0.00021154 9.86427e-5 9.83857e-5 9.80987e-5 | ||
| -0.000210373 -0.000210989 -0.00021154 -9.86427e-5 -9.83857e-5 -9.80987e-5 | ||
| -9.80987e-5 -9.83857e-5 -9.86427e-5 -0.00021154 -0.000210989 -0.000210373</code></pre></div><a class="docs-sourcelink" target="_blank" href="https://github.com/org-arl/SignalAnalysis.jl/blob/fa182dd4c6d63f73d06de96ca6f106cff83d006c/src/array.jl#L28">source</a></section></article></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="tfa.html">« Time-frequency analysis</a><a class="docs-footer-nextpage" href="rand.html">Random noise generation »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 0.27.25 on <span class="colophon-date" title="Saturday 19 August 2023 19:09">Saturday 19 August 2023</span>. Using Julia version 1.6.7.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html> |
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