### A Pluto.jl notebook ###
# v0.19.14

using Markdown
using InteractiveUtils

# ╔═╡ acaedbac-4402-11ed-3b9c-17a6ab36557c
begin
  using Plots
  using LaTeXStrings
  using DSP
  using FFTW
  using Statistics
  # for plotting time-domain discrete sequences
  stem(x, y; kw...) = plot(x, y; legend=false, line=:stem, linecolor=:blue,
                           marker=:circle, markercolor=:blue,
                           markerstrokecolor=:blue, kw...)
  stem(y; kw...) = stem(0:length(y)-1, y; kw...)
  # for plotting frequency-domain discrete sequences
  stemf(x, y; kw...) = plot(x, y; legend=false, line=:stem, linecolor=:blue,
                            marker=:circle, markercolor=:white,
                            markerstrokecolor=:blue, kw...)
  stemf(y; kw...) = stemf(0:length(y)÷2-1, y[1:length(y)÷2]; kw...)
  md"(Some setup code and definitions)"
end

# ╔═╡ c41a9e82-4163-4bdf-a2fa-0376546a1e9b
md"""
Julia versions of some of the numerical demonstrations from Digital Signal Processing (DSP, L314) Michaelmas 2022. Markus Kuhn
"""

# ╔═╡ 4630de8d-5de1-4e63-95cd-a53bcd671878
md"""
# Analog electronics
(slide 4)
"""

# ╔═╡ 85ed177a-5cc8-40d9-b79c-6ae4154b5ab8
let
  L = 1.0
  C = 1.0
  R = 1.0
  Uin = 1.0
  ω = 1e-10:0.01:4
  Uout = Uin * 1.0im ./ (R * (1 ./ (ω*L) - ω*C) .+ 1.0im)
  plot(ω, abs.(Uout); legend=false,
	   xticks = ([1/sqrt(L*C)], [L"1/\sqrt{LC}"]),
	   yticks = ([Uin], [L"U_\mathrm{in}"]),
       xlabel = L"\omega =2\pi f", ylabel = L"$|U_\mathrm{out}|$")
end

# ╔═╡ 54f2d5f8-ed4a-4c67-9991-116db53d86ea
let
	x=zeros(500)
	x[30] = 1
	x[200:350] .= 1
	f = digitalfilter(Bandpass(0.1, 0.12), Butterworth(1))
	plot([x.+0.3,filt(f, x)],
		 label=[L"U_\mathrm{in}" L"U_\mathrm{out}"], xlabel=L"t",
		 xticks=false, yticks=([0, 0.8],[L"U_\mathrm{out}",L"U_\mathrm{in}"]))
end

# ╔═╡ 26a371f9-a77a-4528-a62b-c020f18c1d89
md"""
# Sinusodial sequences
(slide 11)
"""

# ╔═╡ 624ede40-e5b5-4546-acd8-450f3283cf38
let
  n  = 0:40
  fs = 8000
  f  = 400
  φ  = 2π
  x = cos.(2π * f * n/fs .+ φ)
  stem(n, x)
end

# ╔═╡ 20efaf3a-7a12-4c12-8623-5d66cbc799f6
md"""
Try $f=1000, 2000, 3000, 4000, 5000$ Hz. Try negative $f$. Try sine instead of cosine. Try adding phase offsets $\varphi$ of $\pm\frac\pi4$, $\pm\frac\pi2$, and $\pm\pi$.
"""

# ╔═╡ 07d3cb1b-01a8-441a-b731-83519c9ae94e
let
x = [ 0,  0,  0, -4,  0, 0,  0,  0,  0, 0, 2,  2, 2, 2,
      2,  0, -3, -3, -3, 0,  0,  0,  0, 0, 1, -4, 0, 4,
      3, -1,  2, -3, -1, 0,  2, -4, -2, 1, 0,  0, 0, 3,
     -3,  3, -3,  3, -3, 3, -3,  3, -3, 0, 0,  0, 0, 0, 0 ];
y = filt([1, 1, 1, 1]/4, [1], x)
plot([x y],
     linecolor=[:blue :red], markercolor=[:blue :red],
     markershape=[:x :circle], markerstrokewidth=3,
     size = (800, 250), xticks=[], yticks=[0],
     label=["x" "y"], legend=true, ylim=[-7,7])
end

# ╔═╡ dfdfb0a0-a157-4053-90b8-016b54101419
md"""
# Discrete Time Fourier Transform
"""

# ╔═╡ 9a7d108d-b8c3-483d-ae59-46c659dc000a
md"""
    dtft_plot(x::AbstractVector, n1::Int; show_complex=0, show_dft=0)

Plot a finite-support discrete sequence `x`, as well as its Discrete-Time Fourier Transform. Vector `x` contains the sequence elements.

By default the middle element of an odd-length sequence or the first element of an even-length sequence are $x_0$ (i.e., at index $0$). Optional parameter `n1` can be used to set the sequence index of `x[1]`.
"""

# ╔═╡ 016e53cc-919e-4aa1-88b3-95b560869b3b
function dtft_plot(x::AbstractVector,
                   n1=iseven(length(x)) ? 0 : -div(length(x)-1, 2);
                   show_complex=0, show_dft=0, kwargs...)
	l = length(x)
    n = range(n1, length=l)
    nfft = nextpow(2, max(l, 1024))
    x2 = zeros(typeof(x[begin] + 0.0), nfft)
    for i in eachindex(x)
        x2[mod(n1+i-1, nfft) + 1] = x[i];
    end
    f = circshift(fft(x2), div(nfft,2))
    td = plot(n,x; legend=false, line=:stem, marker=:circle)
    w = range(-pi, step=2pi/nfft, length=nfft)
    if show_complex > 0
        fd = plot(w, [real(f) imag(f)]; label=["DTFT real" "DTFT imag"], kwargs...)
    else
        fd = plot(w, abs.(f); label="DTFT mag", kwargs...)
    end
	xticks!(fd, (pi.*(-1.0:0.25:1.0),[L"-\pi", L"-0.75\pi", L"-\pi/2", L"-\pi/4", L"0", L"\pi/4", L"\pi/2", L"0.75\pi", L"\pi"]))
	if show_complex>0; ylims!((-2.2,7.2)); end
    if show_dft > 0
	    wn = 2pi*(0:l-1)/l   # DFT frequencies (positive)
        wn = mod.(wn .+ pi, 2pi) .- pi
		dft = fft(x) .* cis.(-n1*wn) # timeshift DFT output to n1
		if show_complex > 0
            plot!(wn, [real(dft) imag(dft)];
			      line=:stem, marker=:circle, label=["DFT real" "DFT imag"])
		else
			plot!(wn, abs.(dft);
			      line=:stem, marker=:circle, label="DFT mag")
		end
	end
	plot(td, fd; layout=(1, 2), size=(800,300))
end;

# ╔═╡ 0dee1763-9ead-4693-b45d-e6e9367825a4
dtft_plot([0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0]; show_complex=1)

# ╔═╡ 8eeec730-65fb-4c56-b506-ed566e38a0ae
dtft_plot([0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0]; show_complex=1)

# ╔═╡ d06ffc45-2fa3-4d15-a63d-5d4ed8c1536b
dtft_plot([0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0]; show_complex=1)

# ╔═╡ 63493e61-48fb-479f-973c-8dcf0ebf5097
md"""
## Windowing
"""

# ╔═╡ 66ae2ff3-afd0-4753-99d6-56c4ca437482
begin
	n = 255
	padding = 8
	label = ["rect" "triangle" "Hann" "Hamming"]
	b = [Windows.rect(n) Windows.triang(n) Windows.hanning(n) Windows.hamming(n)]
	b = [zeros(padding, size(b,2)); b; zeros(padding, size(b,2))]
	t = 0-padding/(n-1):1/(n-1):1+padding/(n-1)
    plot(t, b; label, xticks=[])
end

# ╔═╡ eb46da1f-5350-4d34-8f52-9fec32bc9024
dtft_plot(cos.(2pi*(0:15)/16*4); show_dft=1, ylims=(-0.1, 8.5))

# ╔═╡ 398e8a64-b950-48aa-888b-32ad90161da8
dtft_plot(cos.(2pi*(0:15)/16*4.2); show_dft=1, ylims=(-0.1, 8.5))

# ╔═╡ b0f80781-8ad2-4218-8042-358230c5e52f
dtft_plot(cos.(2pi*(0:15)/16*4.2) .* Windows.hamming(16); show_dft=1, ylims=(-0.1, 8.5))

# ╔═╡ 6514ae0b-2958-4291-a27c-22694c50d579
dtft_plot(Windows.rect(33); yaxis=:log, ylims=(0.02,40))

# ╔═╡ 95373cb6-945f-451e-998d-17c296423df9
dtft_plot(Windows.triang(33); yaxis=:log, ylims=(0.02,40))

# ╔═╡ fa56b2b3-5d56-4ea0-83ba-79a40171fa82
dtft_plot(Windows.hanning(33); yaxis=:log, ylims=(0.02,40))

# ╔═╡ 8d963f3d-6291-4463-b028-aeab74be175b
dtft_plot(Windows.hamming(33); yaxis=:log, ylims=(0.02,40))

# ╔═╡ 86cbe90a-77f5-4665-8f89-ea69d7a0af5d
md"""
# Example: a single-pole filter
The $z$-transform of the impulse response of an IIR filter is a rational function, which defines a complex-valued surface over the complex plane. The DTFT can be read off there on the unit circle.
"""

# ╔═╡ 190fc757-6c83-4f10-aadd-7a0a5582c97c
let
    b = [0.8];  a = [1, -0.2]
    H(z) = sum(b .* z.^-(eachindex(b).-1)) ./ sum(a .* z.^-(eachindex(a).-1))
    r = nextfloat(-1.0):0.05:1.0   # nextfloat() avoids hitting 0 or 0.2 exactly
    z = r .+ (1im * r')
    u = cis.(2pi * (0:1/64:1))
    plot(real(u), imag(u), zeros(length(u)), label="unit circle")
    scatter!([0],[0],[0], marker=:circle, label="zero");
    scatter!([0],[0.2],[0], marker=:xcross, label="pole");
    plot!(real(u), imag(u), abs.(H.(u)), line=:stem, label="DTFT")
    wireframe!(r, r, min.(abs.(H.(z)),2); camera=(50,15),
               xlabel="real", ylabel="imag", zlabel=L"|H(z)|", zlim=(0,2))
end

# ╔═╡ b4bdd709-54f1-4ca0-999b-cc6011b29082
md"""
## Visual verification
Predict the effect that an IIR filter has on a sinusodial test signal of frequency $f$, by evaluation the $z$-transform of its impulse response on the unit circle, and compare it visually with the result of applying it using the `filt` function.
"""

# ╔═╡ cccbf053-7b75-4751-a407-40f846e3ef2e
let
    n = 0:15;  fs = 8000;
    f = 1500;
    x = cos.(2*pi*f*n/fs);
    b = [0.8];  a = [1, -0.2];
    y1 = filt(b, a, x);
    z = exp.(1im*2*pi*f/fs);
    H = 0.8 * z / (z-0.2);
    A = abs.(H);
    theta = atan.(imag.(H) ./ real.(H));
    y2 = A * cos.(2*pi*f*n/fs.+theta);
    plot(n, [x y1 y2]; color=[:blue :green :red],
	     marker=[:cross :diamond :xcross], markersize=8, markerstrokewidth = 2,
         label=["x" "y (time domain)" "y (z-transform)"],
         ylim=(-1.1, 1.5))
end

# ╔═╡ 662ba58f-ac54-40a1-8a9c-cfe3d1728ba1
md"""
## How do poles affect the time domain?
"""

# ╔═╡ 95623aa6-b4e2-4d50-a14c-829246893747
function zeropole_plot(f::Filters.ZeroPoleGain)
	u = cis.(2pi * (0:1/64:1))
    plot(u; aspect_ratio=:equal, size=(400, 400))
	scatter!(real(f.z), imag(f.z); markers=:circle,
	         markerstrokewidth=2, markersize=6)
    scatter!(real(f.p), imag(f.p); markers=:xcross, markersize=5,
	         markerstrokewidth=4, legend=false,
	         label=["unit circle" "zeros" "poles"])
end

# ╔═╡ 8c31c56e-89fd-4e4f-84e0-e8f304766943
function impulse_response_plot(f)
	x = [1; zeros(31)]
	y = filt(f, x)
	stem(0:length(y)-1, y)
end

# ╔═╡ 57ed2ed3-ba8c-4048-988f-f3599226035f
function filter_plot(f)
	zp = zeropole_plot(f)
	ir = impulse_response_plot(f)
	plot(zp, ir; size=(600,300))
end

# ╔═╡ 164d9fd1-8835-406b-bd6f-ae04f262f6e0
filter_plot(ZeroPoleGain([0.0], [0.7], 1))

# ╔═╡ 35bb671b-d314-4d8f-aa53-fdb02f72ac87
filter_plot(ZeroPoleGain([0.0], [0.9], 1))

# ╔═╡ 042ab4f1-e2db-4d06-96ea-b5f518b77de9
filter_plot(ZeroPoleGain([0.0], [1.0], 1))

# ╔═╡ 44a7ebb5-e268-47d9-9169-2bb037db4fb7
filter_plot(ZeroPoleGain([0.0], [1.1], 1))

# ╔═╡ 130e7ff3-ae1d-43d8-907d-4440ee4b0dd2
filter_plot(ZeroPoleGain([0.0, 0.0], 0.9 * cis.([-1,1] .* pi/6), 1))

# ╔═╡ 0bad950f-6def-473d-9bb0-d9e9b9cf35c7
filter_plot(ZeroPoleGain([0.0, 0.0], 1.0 * cis.([-1,1] .* pi/6), 1))

# ╔═╡ f6f299cf-36b9-438f-9389-649c46132c4a
md"""
## Some IIR filter design methods
"""

# ╔═╡ 977a6687-1ac1-4c39-b7e6-bc146a1529cd
function filter2_plot(f::ZeroPoleGain)
	zp = zeropole_plot(f)
	ir = impulse_response_plot(f)
	H, w = freqresp(f)
	xticks = (pi.*(0:0.25:1.0),[L"0", L"\pi/4", L"\pi/2", L"0.75\pi", L"\pi"])
	fr = plot(w, 20*log10.(abs.(H)); xticks, legend=false,
	          ylabel="amplitude (dB)", ylims=(-50, 3))
	yticks = (pi.*(-1.0:0.25:1.0),[L"-\pi", L"-0.75\pi", L"-\pi/2", L"-\pi/4", L"0", L"\pi/4", L"\pi/2", L"0.75\pi", L"\pi"])
	pr = plot(w, angle.(H); xticks, yticks, legend=false,
	          ylims=(-1,1).*pi, ylabel="phase")
	plot(zp, ir, fr, pr; size=(600,600))
end

# ╔═╡ 8e1470ad-fad9-42ba-9399-c6206c27b3b1
filter2_plot(b::Vector{<:Number}) =
	filter2_plot(convert(ZeroPoleGain, PolynomialRatio(b, [1])))

# ╔═╡ 0d5d9934-3ae2-4371-9d0d-d9d02b75b09a
filter2_plot(digitalfilter(Lowpass(0.3), Butterworth(1)))

# ╔═╡ 8aa9d2e3-d445-438b-8491-d87d14eeef66
filter2_plot(digitalfilter(Lowpass(0.3), Butterworth(5)))

# ╔═╡ 4feeb297-c9d4-4f91-9f03-d18c1a9610f3
filter2_plot(digitalfilter(Lowpass(0.5), Chebyshev1(5, 3)))

# ╔═╡ 85f77adf-9a23-42ef-bd6f-75f5c0bf9f40
filter2_plot(digitalfilter(Lowpass(0.5), Chebyshev2(5, 20)))

# ╔═╡ cf75f102-a156-490e-af6b-db5d8414f2dd
filter2_plot(digitalfilter(Lowpass(0.5), Elliptic(5, 3, 20)))

# ╔═╡ 519ccc83-8c52-40be-99a7-fb45e5540a01
filter2_plot(ZeroPoleGain(cis.(0.25pi.*[-1, 1]), 0.9*cis.(0.25pi.*[-1, 1]), 1))

# ╔═╡ 3bdc232d-22b9-415c-a082-29c10d129c9a
filter2_plot(ZeroPoleGain([-1, 1], 0.9*cis.(0.25pi.*[-1, 1]), 1e-1))

# ╔═╡ 0ae75fa3-6333-44ac-a9c7-01bbe802138c
filter2_plot(digitalfilter(Lowpass(0.25), FIRWindow(hamming(30))))

# ╔═╡ e8a16d5e-a5b9-4bc1-a9f2-a6e526115402
md"""
### Comparison of required filter order
"""

# ╔═╡ 2eba9819-9cc2-4dad-8c4d-967795678e2e
# A Butterworth low-pass filter with a transion band from 0.4*fs/2 to 0.5*fs/2
# with at most 1 dB ripple in the pass band and at least 30 dB attenuation
# in the stop band requires filter order 13
Filters.buttord(0.4, 0.5, 1, 30; domain=:z)

# ╔═╡ d9217802-6293-4d32-a71a-90c3b843129f
# Chebyshev 1/2 filters can do the same in order 6
Filters.cheb1ord(0.4, 0.5, 1, 30; domain=:z)

# ╔═╡ 575012fd-7225-4ed9-930e-42b84cfa98c5
Filters.cheb2ord(0.4, 0.5, 1, 30; domain=:z)

# ╔═╡ b8218263-2c23-4fc3-a6aa-e6c5e64c63ba
# Elliptic can do the same in order 4
Filters.ellipord(0.4, 0.5, 1, 30; domain=:z)

# ╔═╡ 131cd5e2-e190-424d-bc57-8f57ae72571b
# A FIR filter needs order 29
filter2_plot(remez(29, [(0, 0.4) => 1, (0.5, 1.0) => 0]; Hz = 2))

# ╔═╡ 98086cbd-ce41-457c-add4-fe85867df85b
md"""
## Covert spread-spectrum communication demo
"""

# ╔═╡ 772d4275-51c2-476d-a3fe-2906de0a3753
let
    n = randn(10000)
	a = 0.3; l = 1000
	pattern = rand((-a, a), l)
    b0 = [zeros(2000);  pattern; zeros(7000)]
    b1 = [zeros(4000); -pattern; zeros(5000)]
    r = n .+ b0 .+ b1
    f1 = plot([n b0 b1 r] .- [0 -3 -4 -7];
	          label = ["n" "b0" "b1" "r"], yticks=[])
	x = conv(r,reverse(pattern))
	# or: x = xcorr(r,pattern)
    f2 = plot(x; label="xcorr")
	xlims!(f1, 1, length(n)+2*l); xlims!(f2, 1, length(n)+2*l)
	plot(f1, f2; layout=(2,1))
end

# ╔═╡ 39483220-98b2-4404-b660-97d8d2dfd368
md"""
## Covert spread-spectrum radar demo
"""

# ╔═╡ 02056c94-7e84-424d-9b70-25e3edd7bdcd
let
    x = randn(10000)
    h = [0, 0, 0.4, 0, 0, 0.3, 0, 0, 0.2, 0, 0];
    y = conv(x, h);
    f1 = plot(1:length(x), x;      label = "x beam")
	plot!(f1, 1:length(y), y .- 5, label = "y return", yticks=[]);
    c = conv(reverse(x),y);
	lags = -20:20
    f2 = stem(lags, c[length(c)÷2 .+ lags]);
    plot(f1, f2; layout=(2,1))
end

# ╔═╡ 0c350605-fa57-4488-a074-dc7e92f1442b
md"""
## Spectral estimation
"""

# ╔═╡ da2607e6-e7a2-4ad4-b28f-380035c4097e
let
    n = 64    # block length
    m = 1000  # blocks averaged
    k = 1:(n*m)
    x = randn(n*m) +
        sin.(2*pi*k *  8.00 ./ n) +
        sin.(2*pi*k * 14.32 ./ n)
    xx = reshape(x, n, m)

	s1 = abs.(fft(x[1:n])/n)
	s2 = abs.(fft(x[1:8n])/8n)
    s3 = mean(abs.(fft(xx, 1)/n),dims=2)
    s4 = abs.(mean(fft(xx, 1)/n,dims=2))
	plots = stemf.([s1,s2,s3,s4];
	               ylims=(0, 0.75), yticks = [0]);
    plot(plots...)
end

# ╔═╡ 0e38d1bf-765c-4687-a385-33db2a67d78d
# Lookup table to map slide framenumberlabel to slide number, generated with
# perl -nE 'BEGIN{print("Dict("),}END{print(")")}/^\\newlabel\{(.+?)\}\{\{(\d+)\}\{/ && print "\"$1\"=>$2,"' dsp-slides.aux
begin
slide=Dict("ref:impulse-sequence"=>10,"weberfechner"=>14,"lti-avr"=>19,"lti-exp"=>20,"lti-acc"=>21,"lti-diff"=>22,"ref:direct-form1"=>25,"convolution<1>"=>26,"convolution"=>26,"convolution<2>"=>27,"convolution<3>"=>27,"convolution<4>"=>28,"convolution<5>"=>28,"stars"=>31,"hz"=>38,"diracprop"=>48,"am"=>53,"ex:dac"=>7,"ex:sampling"=>10,"deconv"=>86,"deconv-noise"=>88,"ex:dtmf"=>14,"ztransform"=>118,"ex:ztrans"=>16,"iqdown"=>166,"fmdemo1"=>19,"dct2bases"=>218,)
nothing
end

# ╔═╡ 006e7bf0-8423-4399-9545-7a943effd13e
md"""
# $M$-point moving average system
(slide $(slide["lti-avr"]))
"""

# ╔═╡ 00000000-0000-0000-0000-000000000001
PLUTO_PROJECT_TOML_CONTENTS = """
[deps]
DSP = "717857b8-e6f2-59f4-9121-6e50c889abd2"
FFTW = "7a1cc6ca-52ef-59f5-83cd-3a7055c09341"
LaTeXStrings = "b964fa9f-0449-5b57-a5c2-d3ea65f4040f"
Plots = "91a5bcdd-55d7-5caf-9e0b-520d859cae80"
Statistics = "10745b16-79ce-11e8-11f9-7d13ad32a3b2"

[compat]
DSP = "~0.7.7"
FFTW = "~1.5.0"
LaTeXStrings = "~1.3.0"
Plots = "~1.35.2"
"""

# ╔═╡ 00000000-0000-0000-0000-000000000002
PLUTO_MANIFEST_TOML_CONTENTS = """
# This file is machine-generated - editing it directly is not advised

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git-tree-sha1 = "e78d10aab01a4a154142c5006ed44fd9e8e31b67"
uuid = "c22f9ab0-d5fe-5066-847c-f4bb1cd4e361"
version = "0.4.1+1"

[[deps.Xorg_xkbcomp_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libxkbfile_jll"]
git-tree-sha1 = "4bcbf660f6c2e714f87e960a171b119d06ee163b"
uuid = "35661453-b289-5fab-8a00-3d9160c6a3a4"
version = "1.4.2+4"

[[deps.Xorg_xkeyboard_config_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_xkbcomp_jll"]
git-tree-sha1 = "5c8424f8a67c3f2209646d4425f3d415fee5931d"
uuid = "33bec58e-1273-512f-9401-5d533626f822"
version = "2.27.0+4"

[[deps.Xorg_xtrans_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "79c31e7844f6ecf779705fbc12146eb190b7d845"
uuid = "c5fb5394-a638-5e4d-96e5-b29de1b5cf10"
version = "1.4.0+3"

[[deps.Zlib_jll]]
deps = ["Libdl"]
uuid = "83775a58-1f1d-513f-b197-d71354ab007a"
version = "1.2.12+3"

[[deps.Zstd_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "e45044cd873ded54b6a5bac0eb5c971392cf1927"
uuid = "3161d3a3-bdf6-5164-811a-617609db77b4"
version = "1.5.2+0"

[[deps.fzf_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "868e669ccb12ba16eaf50cb2957ee2ff61261c56"
uuid = "214eeab7-80f7-51ab-84ad-2988db7cef09"
version = "0.29.0+0"

[[deps.libaom_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "3a2ea60308f0996d26f1e5354e10c24e9ef905d4"
uuid = "a4ae2306-e953-59d6-aa16-d00cac43593b"
version = "3.4.0+0"

[[deps.libass_jll]]
deps = ["Artifacts", "Bzip2_jll", "FreeType2_jll", "FriBidi_jll", "HarfBuzz_jll", "JLLWrappers", "Libdl", "Pkg", "Zlib_jll"]
git-tree-sha1 = "5982a94fcba20f02f42ace44b9894ee2b140fe47"
uuid = "0ac62f75-1d6f-5e53-bd7c-93b484bb37c0"
version = "0.15.1+0"

[[deps.libblastrampoline_jll]]
deps = ["Artifacts", "Libdl", "OpenBLAS_jll"]
uuid = "8e850b90-86db-534c-a0d3-1478176c7d93"
version = "5.1.1+0"

[[deps.libfdk_aac_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "daacc84a041563f965be61859a36e17c4e4fcd55"
uuid = "f638f0a6-7fb0-5443-88ba-1cc74229b280"
version = "2.0.2+0"

[[deps.libpng_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Zlib_jll"]
git-tree-sha1 = "94d180a6d2b5e55e447e2d27a29ed04fe79eb30c"
uuid = "b53b4c65-9356-5827-b1ea-8c7a1a84506f"
version = "1.6.38+0"

[[deps.libvorbis_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Ogg_jll", "Pkg"]
git-tree-sha1 = "b910cb81ef3fe6e78bf6acee440bda86fd6ae00c"
uuid = "f27f6e37-5d2b-51aa-960f-b287f2bc3b7a"
version = "1.3.7+1"

[[deps.nghttp2_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "8e850ede-7688-5339-a07c-302acd2aaf8d"
version = "1.48.0+0"

[[deps.p7zip_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "3f19e933-33d8-53b3-aaab-bd5110c3b7a0"
version = "17.4.0+0"

[[deps.x264_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "4fea590b89e6ec504593146bf8b988b2c00922b2"
uuid = "1270edf5-f2f9-52d2-97e9-ab00b5d0237a"
version = "2021.5.5+0"

[[deps.x265_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "ee567a171cce03570d77ad3a43e90218e38937a9"
uuid = "dfaa095f-4041-5dcd-9319-2fabd8486b76"
version = "3.5.0+0"

[[deps.xkbcommon_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Wayland_jll", "Wayland_protocols_jll", "Xorg_libxcb_jll", "Xorg_xkeyboard_config_jll"]
git-tree-sha1 = "9ebfc140cc56e8c2156a15ceac2f0302e327ac0a"
uuid = "d8fb68d0-12a3-5cfd-a85a-d49703b185fd"
version = "1.4.1+0"
"""

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