### A Pluto.jl notebook ###
# v1.0.3

using Markdown
using InteractiveUtils

# This Pluto notebook uses @bind for interactivity. When running this notebook outside of Pluto, the following 'mock version' of @bind gives bound variables a default value (instead of an error).
macro bind(def, element)
    #! format: off
    return quote
        local iv = try Base.loaded_modules[Base.PkgId(Base.UUID("6e696c72-6542-2067-7265-42206c756150"), "AbstractPlutoDingetjes")].Bonds.initial_value catch; b -> missing; end
        local el = $(esc(element))
        global $(esc(def)) = Core.applicable(Base.get, el) ? Base.get(el) : iv(el)
        el
    end
    #! format: on
end

# ╔═╡ acaedbac-4402-11ed-3b9c-17a6ab36557c
begin
    #using Pkg; Pkg.update()
    using Plots
    using Plots.PlotMeasures  # for the `mm` unit (or write Plots.mm)
    using LaTeXStrings
    using DSP
    using FFTW
    using Statistics
    using Printf
    # increase font sizes in all plots by 20%
    Plots.resetfontsizes()
    Plots.scalefontsizes(1.2)
    # 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...)
    # for plotting FFT input/outputs
    fftplot(f, x; kw...) =
        plot(circshift(f, length(f)÷2), circshift(x, length(x)÷2);
             label=false, 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 2026. Markus Kuhn
"""

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

An analog RLC band-pass filter, consisting of resistor ``R`` in series with a parallel ``LC`` circuit:

```math
\frac{U_\mathrm{in}-U_\mathrm{out}}{R} =
\frac1L\int_{-\infty}^t U_\mathrm{out}\,\mathrm{d}\tau +
C\frac{\mathrm{d}U_\mathrm{out}}{\mathrm{d}t}
```
"""

# ╔═╡ b95c0a44-7649-46ca-9229-27d4e176d7d5
md"""
(slide 32)

An analog ``RC`` filter:

```math
\frac{U_\mathrm{in}-U_\mathrm{out}}{R} =
C\frac{\mathrm{d}U_\mathrm{out}}{\mathrm{d}t}
```
"""

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

# ╔═╡ 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 is $x_0$ (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
let
    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"""
# IIR 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 sinusoidal test signal of frequency $f$, by evaluating 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; kw...)
    u = cis.(2pi * (0:1/64:1))
    plot(u; aspect_ratio=:equal, size=(400, 400), label="unit circle")
    scatter!(real(f.z), imag(f.z); markers=:circle, markersize=6,
             markerstrokewidth=2, label="zeros")
    scatter!(real(f.p), imag(f.p); markers=:xcross, markersize=5,
             markerstrokewidth=4, label="poles", legend=false, kw...)
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), bottom_margin=3mm)
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

# ╔═╡ 992ddca1-7e69-4521-aa74-1795b88a2e45
md"""
## Butterworth filter (order 1)
"""

# ╔═╡ 018ec4b5-9bc0-46c9-9559-306adb2c3308
md"""
## Butterworth filter (order 5)
"""

# ╔═╡ 76e95a11-f0b8-4a1d-8726-5525ca4555ba
md"""
## Chebyshev filter (type I)
"""

# ╔═╡ e19f5d17-2e25-4a0b-b59f-f8755456cf25
md"""
## Chebyshev filter (type II)
"""

# ╔═╡ 70cdad35-2c3f-4b21-b743-2029bfc6622b
md"""
## Elliptic filter
"""

# ╔═╡ 016b2e85-fa42-438d-8867-f5ae2dfc20ca
md"""
## Notch filter
"""

# ╔═╡ 443b6594-c50f-429e-a21e-a145808986ba
md"""
## Peak filter
"""

# ╔═╡ 8621a483-4db2-4e29-91f6-fdf0a06e4966
md"""
## Window-based FIR filter (order 30, i.e. 31 taps)
"""

# ╔═╡ 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(31))))

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

# ╔═╡ 2eba9819-9cc2-4dad-8c4d-967795678e2e
# A Butterworth low-pass filter with a transition 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
# An FIR filter needs 29 taps, i.e. order 28 (28 taps reach only 29.4 dB)
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, f2), 1, length(n)+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)-length(h))÷2 .+ lags .+ 1]);
    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

# ╔═╡ 2b63af4a-344b-4e8c-9f44-462c5d031fd7
md"## Raised-cosine filter"

# ╔═╡ 14adc351-3e39-4b4a-81ca-3df154d109f5
function raised_cosine(f, T, beta)
    if abs(f) <= (1-beta)/(2T)
        return T
    elseif abs(f) <= (1+beta)/(2T)
        return 0.5T*(1.0 + cos(pi*T/beta*(abs(f)-(1-beta)/(2T))))
    else
        return 0.0
    end
end;

# ╔═╡ 1e0dd8f8-0bfd-4692-b8ac-4ebfc6c67e7f
@bind beta_slider html"Choose roll-off factor β: <input type=range>"

# ╔═╡ bbcd399b-b3d5-4a0a-b516-d5d8bc4316ac
let
    n = 2048     # FFT block size
    beta = beta_slider/100   # roll-off factor
    if ismissing(beta) ; beta = 0.5 ; end
    d = 16
    fn = n ÷ d   # Nyquist frequency index 1/(2T) / (fs/n)
    fs = 1
    T = n/(2*fn*fs)
    Ts = d÷2     # = T/fs  symbol period in samples
    nn = vcat(0:(n÷2-1),(-n÷2):-1)
    f = (fs/n).*nn
    X = raised_cosine.(f, T, beta)
    # X = sqrt.(X)  # root raised cosine
    p1 = fftplot(f, X; title=@sprintf("β = %0.2f", beta),
                 gridalpha=0.3, xlim=[-3/d,3/d],
                 xticks=([-1/d, 1/d], ["−1/(2T)", "1/(2T)"]),
                 yticks=([0.0, 0.5T, T], ["0", "T/2", "T"]))
    x = ifft(X)
    # xx = zero(x) ; for i = -4:4; xx += circshift(x, Ts*i); end; x = xx
    p2 = fftplot(nn, real.(x); xlim=[-4d, 4d], ylim=[-0.25, 1.25],
                 xticks=(-4d:d÷2:4d, ["$(i)T" for i=-d÷2:d÷2]),
                 gridalpha=0.3)
    plot(p1, p2; layout=(2,1))
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"]))
"""

# ╔═╡ ba7277c4-8750-4239-98cc-d3f9f42ddd21
# @fig "exampleplot" plot(sin)
# Saves the plot in file "$_figdir/exampleplot.pdf" if the global
# string constant _figdir is defined, for example if run with
# julia --project -e 'const _figdir="nbfigs";include("dsp-notebook.jl")'
# If the global variable _onlypath is defined, only save the figure
# if the resulting saved file path matches _onlypath.
begin
    macro fig(filename, plot)
        return :(
            let p, path
                if @isdefined(_figdir)
                    path = joinpath(_figdir, $filename * ".pdf")
                    if !@isdefined(_onlypath) || _onlypath == path
                        p = $plot;
                        savefig(p, path)
                        p
                    end
                else
                    $plot
                end
            end
        )
    end
    nothing
end

# ╔═╡ 85ed177a-5cc8-40d9-b79c-6ae4154b5ab8
@fig "analog" let
    # circuit parameters
    L = 1.0
    C = 1.0
    R = 5.0
    Uin = 1.0
    # frequency-domain response
    ω = 1e-10:0.01:4
    Uout = Uin * 1.0im ./ (R * (1 ./ (ω*L) - ω*C) .+ 1.0im)
    pf = plot(ω, abs.(Uout); legend=false, color=:black,
              xticks = ([1/sqrt(L*C)], [L"1/\sqrt{LC}"]),
              yticks = ([Uin], [L"U_\mathrm{in}"]),
              xlabel = L"\omega\qquad(2\pi f)", ylabel = L"$|U_\mathrm{out}|$")
    # time-domain response
    x=zeros(500)
    x[30] = 1
    x[200:350] .= 1
    f = digitalfilter(Bandpass(0.1, 0.12), Butterworth(1))
    pt = plot([x.+0.3,filt(f, x)]; legend=false, color=:black,
              label=[L"U_\mathrm{in}" L"U_\mathrm{out}"], xlabel=L"t",
              xticks=false, yticks=([0, 0.3],[L"U_\mathrm{out}",L"U_\mathrm{in}"]))
    pt[1][:yaxis][:tickfontsize] = pt[1][:yaxis][:guidefontsize]

    plot(pf, pt; layout=(2,1), size=0.6.*(600,2*400), left_margin=3mm)
end

# ╔═╡ 92c16957-3e16-42eb-8c18-ee01e71c72c1
@fig "analog2" let
	C=1.0
	R=1.0
	Uin=1.0
	# frequency-domain response
	ω = 1e-10:0.01:4;
	Uout = Uin * 1im ./ sqrt.(1 .+ (ω * R * C).^2)
	pf = plot(ω, abs.(Uout); legend=false, color=:black,
              xticks = ([1/(R*C)], [L"1/RC"]),
              yticks = ([Uin], [L"U_\mathrm{in}"]),
              xlabel = L"\omega\qquad(2\pi f)", ylabel = L"$|U_\mathrm{out}|$")
	# time-domain response
	x=zeros(500)
    x[[30,120,140,160,170,180,190]] .= 5
    x[250:400] .= 1
    f = digitalfilter(Lowpass(0.02), Butterworth(1))
    pt = plot([x.+1.5,filt(f, x)]; legend=false, color=:black, size=0.6.*(600,400),
              label=[L"U_\mathrm{in}" L"U_\mathrm{out}"], xlabel=L"t",
              xticks=false, yticks=([0, 1.5],[L"U_\mathrm{out}",L"U_\mathrm{in}"]))
	pt[1][:yaxis][:tickfontsize] = pt[1][:yaxis][:guidefontsize]
	pt
end

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

# ╔═╡ 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"
Printf = "de0858da-6303-5e67-8744-51eddeeeb8d7"
Statistics = "10745b16-79ce-11e8-11f9-7d13ad32a3b2"

[compat]
DSP = "~0.8.6"
FFTW = "~1.10.0"
LaTeXStrings = "~1.4.1"
Plots = "~1.41.7"
"""

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

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    AbstractFFTsTestExt = "Test"

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[[deps.Colors]]
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[[deps.DataAPI]]
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deps = ["IrrationalConstants", "LogExpFunctions", "OpenLibm_jll", "OpenSpecFun_jll"]
git-tree-sha1 = "429071b23f4c9a13fb6582f807cc2ef454082408"
uuid = "276daf66-3868-5448-9aa4-cd146d93841b"
version = "2.9.0"

    [deps.SpecialFunctions.extensions]
    SpecialFunctionsChainRulesCoreExt = "ChainRulesCore"

    [deps.SpecialFunctions.weakdeps]
    ChainRulesCore = "d360d2e6-b24c-11e9-a2a3-2a2ae2dbcce4"

[[deps.StableRNGs]]
deps = ["Random"]
git-tree-sha1 = "4f96c596b8c8258cc7d3b19797854d368f243ddc"
uuid = "860ef19b-820b-49d6-a774-d7a799459cd3"
version = "1.0.4"

[[deps.StaticArraysCore]]
git-tree-sha1 = "6ab403037779dae8c514bad259f32a447262455a"
uuid = "1e83bf80-4336-4d27-bf5d-d5a4f845583c"
version = "1.4.4"

[[deps.Statistics]]
deps = ["LinearAlgebra", "SparseArrays"]
uuid = "10745b16-79ce-11e8-11f9-7d13ad32a3b2"
version = "1.10.0"

[[deps.StatsAPI]]
deps = ["LinearAlgebra"]
git-tree-sha1 = "178ed29fd5b2a2cfc3bd31c13375ae925623ff36"
uuid = "82ae8749-77ed-4fe6-ae5f-f523153014b0"
version = "1.8.0"

[[deps.StatsBase]]
deps = ["AliasTables", "DataAPI", "DataStructures", "IrrationalConstants", "LinearAlgebra", "LogExpFunctions", "Missings", "Printf", "Random", "SortingAlgorithms", "SparseArrays", "Statistics", "StatsAPI"]
git-tree-sha1 = "adb9da019510162e67a4493fc235c23203d8b09e"
uuid = "2913bbd2-ae8a-5f71-8c99-4fb6c76f3a91"
version = "0.34.13"

[[deps.StructUtils]]
deps = ["Dates", "UUIDs"]
git-tree-sha1 = "2d0fc55c61321ba245c47be599570d11bac50303"
uuid = "ec057cc2-7a8d-4b58-b3b3-92acb9f63b42"
version = "2.8.5"

    [deps.StructUtils.extensions]
    StructUtilsMeasurementsExt = ["Measurements"]
    StructUtilsStaticArraysCoreExt = ["StaticArraysCore"]
    StructUtilsTablesExt = ["Tables"]

    [deps.StructUtils.weakdeps]
    Measurements = "eff96d63-e80a-5855-80a2-b1b0885c5ab7"
    StaticArraysCore = "1e83bf80-4336-4d27-bf5d-d5a4f845583c"
    Tables = "bd369af6-aec1-5ad0-b16a-f7cc5008161c"

[[deps.SuiteSparse_jll]]
deps = ["Artifacts", "Libdl", "libblastrampoline_jll"]
uuid = "bea87d4a-7f5b-5778-9afe-8cc45184846c"
version = "7.2.1+1"

[[deps.TOML]]
deps = ["Dates"]
uuid = "fa267f1f-6049-4f14-aa54-33bafae1ed76"
version = "1.0.3"

[[deps.Tar]]
deps = ["ArgTools", "SHA"]
uuid = "a4e569a6-e804-4fa4-b0f3-eef7a1d5b13e"
version = "1.10.0"

[[deps.TensorCore]]
deps = ["LinearAlgebra"]
git-tree-sha1 = "1feb45f88d133a655e001435632f019a9a1bcdb6"
uuid = "62fd8b95-f654-4bbd-a8a5-9c27f68ccd50"
version = "0.1.1"

[[deps.Test]]
deps = ["InteractiveUtils", "Logging", "Random", "Serialization"]
uuid = "8dfed614-e22c-5e08-85e1-65c5234f0b40"

[[deps.UUIDs]]
deps = ["Random", "SHA"]
uuid = "cf7118a7-6976-5b1a-9a39-7adc72f591a4"

[[deps.Unicode]]
uuid = "4ec0a83e-493e-50e2-b9ac-8f72acf5a8f5"

[[deps.UnicodeFun]]
deps = ["REPL"]
git-tree-sha1 = "53915e50200959667e78a92a418594b428dffddf"
uuid = "1cfade01-22cf-5700-b092-accc4b62d6e1"
version = "0.4.1"

[[deps.Unzip]]
git-tree-sha1 = "ca0969166a028236229f63514992fc073799bb78"
uuid = "41fe7b60-77ed-43a1-b4f0-825fd5a5650d"
version = "0.2.0"

[[deps.Vulkan_Loader_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Wayland_jll", "Xorg_libX11_jll", "Xorg_libXrandr_jll", "xkbcommon_jll"]
git-tree-sha1 = "2f0486047a07670caad3a81a075d2e518acc5c59"
uuid = "a44049a8-05dd-5a78-86c9-5fde0876e88c"
version = "1.3.243+0"

[[deps.Wayland_jll]]
deps = ["Artifacts", "EpollShim_jll", "Expat_jll", "JLLWrappers", "Libdl", "Libffi_jll"]
git-tree-sha1 = "96478df35bbc2f3e1e791bc7a3d0eeee559e60e9"
uuid = "a2964d1f-97da-50d4-b82a-358c7fce9d89"
version = "1.24.0+0"

[[deps.XZ_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "b29c22e245d092b8b4e8d3c09ad7baa586d9f573"
uuid = "ffd25f8a-64ca-5728-b0f7-c24cf3aae800"
version = "5.8.3+0"

[[deps.Xorg_libICE_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "a3ea76ee3f4facd7a64684f9af25310825ee3668"
uuid = "f67eecfb-183a-506d-b269-f58e52b52d7c"
version = "1.1.2+0"

[[deps.Xorg_libSM_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Xorg_libICE_jll"]
git-tree-sha1 = "9c7ad99c629a44f81e7799eb05ec2746abb5d588"
uuid = "c834827a-8449-5923-a945-d239c165b7dd"
version = "1.2.6+0"

[[deps.Xorg_libX11_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Xorg_libxcb_jll", "Xorg_xtrans_jll"]
git-tree-sha1 = "808090ede1d41644447dd5cbafced4731c56bd2f"
uuid = "4f6342f7-b3d2-589e-9d20-edeb45f2b2bc"
version = "1.8.13+0"

[[deps.Xorg_libXau_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "aa1261ebbac3ccc8d16558ae6799524c450ed16b"
uuid = "0c0b7dd1-d40b-584c-a123-a41640f87eec"
version = "1.0.13+0"

[[deps.Xorg_libXcursor_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Xorg_libXfixes_jll", "Xorg_libXrender_jll"]
git-tree-sha1 = "6c74ca84bbabc18c4547014765d194ff0b4dc9da"
uuid = "935fb764-8cf2-53bf-bb30-45bb1f8bf724"
version = "1.2.4+0"

[[deps.Xorg_libXdmcp_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "52858d64353db33a56e13c341d7bf44cd0d7b309"
uuid = "a3789734-cfe1-5b06-b2d0-1dd0d9d62d05"
version = "1.1.6+0"

[[deps.Xorg_libXext_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Xorg_libX11_jll"]
git-tree-sha1 = "1a4a26870bf1e5d26cd585e38038d399d7e65706"
uuid = "1082639a-0dae-5f34-9b06-72781eeb8cb3"
version = "1.3.8+0"

[[deps.Xorg_libXfixes_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Xorg_libX11_jll"]
git-tree-sha1 = "75e00946e43621e09d431d9b95818ee751e6b2ef"
uuid = "d091e8ba-531a-589c-9de9-94069b037ed8"
version = "6.0.2+0"

[[deps.Xorg_libXi_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Xorg_libXext_jll", "Xorg_libXfixes_jll"]
git-tree-sha1 = "dcb316b3ce0941f195537dda56bea4517fcd3ff5"
uuid = "a51aa0fd-4e3c-5386-b890-e753decda492"
version = "1.8.4+0"

[[deps.Xorg_libXinerama_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Xorg_libXext_jll"]
git-tree-sha1 = "0ba01bc7396896a4ace8aab67db31403c71628f4"
uuid = "d1454406-59df-5ea1-beac-c340f2130bc3"
version = "1.1.7+0"

[[deps.Xorg_libXrandr_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Xorg_libXext_jll", "Xorg_libXrender_jll"]
git-tree-sha1 = "6c174ef70c96c76f4c3f4d3cfbe09d018bcd1b53"
uuid = "ec84b674-ba8e-5d96-8ba1-2a689ba10484"
version = "1.5.6+0"

[[deps.Xorg_libXrender_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Xorg_libX11_jll"]
git-tree-sha1 = "7ed9347888fac59a618302ee38216dd0379c480d"
uuid = "ea2f1a96-1ddc-540d-b46f-429655e07cfa"
version = "0.9.12+0"

[[deps.Xorg_libpciaccess_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Zlib_jll"]
git-tree-sha1 = "58972370b81423fc546c56a60ed1a009450177c3"
uuid = "a65dc6b1-eb27-53a1-bb3e-dea574b5389e"
version = "0.19.0+0"

[[deps.Xorg_libxcb_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Xorg_libXau_jll", "Xorg_libXdmcp_jll"]
git-tree-sha1 = "bfcaf7ec088eaba362093393fe11aa141fa15422"
uuid = "c7cfdc94-dc32-55de-ac96-5a1b8d977c5b"
version = "1.17.1+0"

[[deps.Xorg_libxkbfile_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Xorg_libX11_jll"]
git-tree-sha1 = "ed756a03e95fff88d8f738ebc2849431bdd4fd1a"
uuid = "cc61e674-0454-545c-8b26-ed2c68acab7a"
version = "1.2.0+0"

[[deps.Xorg_xcb_util_cursor_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Xorg_xcb_util_image_jll", "Xorg_xcb_util_jll", "Xorg_xcb_util_renderutil_jll"]
git-tree-sha1 = "9750dc53819eba4e9a20be42349a6d3b86c7cdf8"
uuid = "e920d4aa-a673-5f3a-b3d7-f755a4d47c43"
version = "0.1.6+0"

[[deps.Xorg_xcb_util_image_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Xorg_xcb_util_jll"]
git-tree-sha1 = "f4fc02e384b74418679983a97385644b67e1263b"
uuid = "12413925-8142-5f55-bb0e-6d7ca50bb09b"
version = "0.4.1+0"

[[deps.Xorg_xcb_util_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Xorg_libxcb_jll"]
git-tree-sha1 = "68da27247e7d8d8dafd1fcf0c3654ad6506f5f97"
uuid = "2def613f-5ad1-5310-b15b-b15d46f528f5"
version = "0.4.1+0"

[[deps.Xorg_xcb_util_keysyms_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Xorg_xcb_util_jll"]
git-tree-sha1 = "44ec54b0e2acd408b0fb361e1e9244c60c9c3dd4"
uuid = "975044d2-76e6-5fbe-bf08-97ce7c6574c7"
version = "0.4.1+0"

[[deps.Xorg_xcb_util_renderutil_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Xorg_xcb_util_jll"]
git-tree-sha1 = "5b0263b6d080716a02544c55fdff2c8d7f9a16a0"
uuid = "0d47668e-0667-5a69-a72c-f761630bfb7e"
version = "0.3.10+0"

[[deps.Xorg_xcb_util_wm_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Xorg_xcb_util_jll"]
git-tree-sha1 = "f233c83cad1fa0e70b7771e0e21b061a116f2763"
uuid = "c22f9ab0-d5fe-5066-847c-f4bb1cd4e361"
version = "0.4.2+0"

[[deps.Xorg_xkbcomp_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Xorg_libxkbfile_jll"]
git-tree-sha1 = "801a858fc9fb90c11ffddee1801bb06a738bda9b"
uuid = "35661453-b289-5fab-8a00-3d9160c6a3a4"
version = "1.4.7+0"

[[deps.Xorg_xkeyboard_config_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Xorg_xkbcomp_jll"]
git-tree-sha1 = "2e59214e017a55cb87474a00fa76035c82ac0e17"
uuid = "33bec58e-1273-512f-9401-5d533626f822"
version = "2.47.0+2"

[[deps.Xorg_xtrans_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "a63799ff68005991f9d9491b6e95bd3478d783cb"
uuid = "c5fb5394-a638-5e4d-96e5-b29de1b5cf10"
version = "1.6.0+0"

[[deps.Zlib_jll]]
deps = ["Libdl"]
uuid = "83775a58-1f1d-513f-b197-d71354ab007a"
version = "1.2.13+1"

[[deps.Zstd_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "446b23e73536f84e8037f5dce465e92275f6a308"
uuid = "3161d3a3-bdf6-5164-811a-617609db77b4"
version = "1.5.7+1"

[[deps.eudev_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "c3b0e6196d50eab0c5ed34021aaa0bb463489510"
uuid = "35ca27e7-8b34-5b7f-bca9-bdc33f59eb06"
version = "3.2.14+0"

[[deps.fzf_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "b6a34e0e0960190ac2a4363a1bd003504772d631"
uuid = "214eeab7-80f7-51ab-84ad-2988db7cef09"
version = "0.61.1+0"

[[deps.libaom_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "ef17c47d22224aaecc76e597ab21a072e025cf7b"
uuid = "a4ae2306-e953-59d6-aa16-d00cac43593b"
version = "3.14.1+0"

[[deps.libass_jll]]
deps = ["Artifacts", "Bzip2_jll", "FreeType2_jll", "FriBidi_jll", "HarfBuzz_jll", "JLLWrappers", "Libdl", "Zlib_jll"]
git-tree-sha1 = "cb007192783c56d8249db4cf0e3495001edfe414"
uuid = "0ac62f75-1d6f-5e53-bd7c-93b484bb37c0"
version = "0.17.5+0"

[[deps.libblastrampoline_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "8e850b90-86db-534c-a0d3-1478176c7d93"
version = "5.11.0+0"

[[deps.libdecor_jll]]
deps = ["Artifacts", "Dbus_jll", "JLLWrappers", "Libdl", "Libglvnd_jll", "Pango_jll", "Wayland_jll", "xkbcommon_jll"]
git-tree-sha1 = "9bf7903af251d2050b467f76bdbe57ce541f7f4f"
uuid = "1183f4f0-6f2a-5f1a-908b-139f9cdfea6f"
version = "0.2.2+0"

[[deps.libdrm_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Xorg_libpciaccess_jll"]
git-tree-sha1 = "28e57478e8a160d346a19c28b3fffb9273bcc9c2"
uuid = "8e53e030-5e6c-5a89-a30b-be5b7263a166"
version = "2.4.134+0"

[[deps.libevdev_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "56d643b57b188d30cccc25e331d416d3d358e557"
uuid = "2db6ffa8-e38f-5e21-84af-90c45d0032cc"
version = "1.13.4+0"

[[deps.libfdk_aac_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "646634dd19587a56ee2f1199563ec056c5f228df"
uuid = "f638f0a6-7fb0-5443-88ba-1cc74229b280"
version = "2.0.4+0"

[[deps.libinput_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "eudev_jll", "libevdev_jll", "mtdev_jll"]
git-tree-sha1 = "91d05d7f4a9f67205bd6cf395e488009fe85b499"
uuid = "36db933b-70db-51c0-b978-0f229ee0e533"
version = "1.28.1+0"

[[deps.libpng_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Zlib_jll"]
git-tree-sha1 = "e51150d5ab85cee6fc36726850f0e627ad2e4aba"
uuid = "b53b4c65-9356-5827-b1ea-8c7a1a84506f"
version = "1.6.58+0"

[[deps.libva_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Xorg_libX11_jll", "Xorg_libXext_jll", "Xorg_libXfixes_jll", "libdrm_jll"]
git-tree-sha1 = "7dbf96baae3310fe2fa0df0ccbb3c6288d5816c9"
uuid = "9a156e7d-b971-5f62-b2c9-67348b8fb97c"
version = "2.23.0+0"

[[deps.libvorbis_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Ogg_jll"]
git-tree-sha1 = "11e1772e7f3cc987e9d3de991dd4f6b2602663a5"
uuid = "f27f6e37-5d2b-51aa-960f-b287f2bc3b7a"
version = "1.3.8+0"

[[deps.mtdev_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "b4d631fd51f2e9cdd93724ae25b2efc198b059b1"
uuid = "009596ad-96f7-51b1-9f1b-5ce2d5e8a71e"
version = "1.1.7+0"

[[deps.nghttp2_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "8e850ede-7688-5339-a07c-302acd2aaf8d"
version = "1.52.0+1"

[[deps.oneTBB_jll]]
deps = ["Artifacts", "JLLWrappers", "LazyArtifacts", "Libdl"]
git-tree-sha1 = "da8c1f6eee04831f14edcfa5dae611d309807e57"
uuid = "1317d2d5-d96f-522e-a858-c73665f53c3e"
version = "2022.3.0+0"

[[deps.p7zip_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "3f19e933-33d8-53b3-aaab-bd5110c3b7a0"
version = "17.6.1+0"

[[deps.x264_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "14cc7083fc6dff3cc44f2bc435ee96d06ed79aa7"
uuid = "1270edf5-f2f9-52d2-97e9-ab00b5d0237a"
version = "10164.0.1+0"

[[deps.x265_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "e7b67590c14d487e734dcb925924c5dc43ec85f3"
uuid = "dfaa095f-4041-5dcd-9319-2fabd8486b76"
version = "4.1.0+0"

[[deps.xkbcommon_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Xorg_libxcb_jll", "Xorg_xkeyboard_config_jll"]
git-tree-sha1 = "a1fc6507a40bf504527d0d4067d718f8e179b2b8"
uuid = "d8fb68d0-12a3-5cfd-a85a-d49703b185fd"
version = "1.13.0+0"
"""

# ╔═╡ Cell order:
# ╟─c41a9e82-4163-4bdf-a2fa-0376546a1e9b
# ╟─4630de8d-5de1-4e63-95cd-a53bcd671878
# ╟─85ed177a-5cc8-40d9-b79c-6ae4154b5ab8
# ╟─b95c0a44-7649-46ca-9229-27d4e176d7d5
# ╟─92c16957-3e16-42eb-8c18-ee01e71c72c1
# ╟─26a371f9-a77a-4528-a62b-c020f18c1d89
# ╠═624ede40-e5b5-4546-acd8-450f3283cf38
# ╟─20efaf3a-7a12-4c12-8623-5d66cbc799f6
# ╟─006e7bf0-8423-4399-9545-7a943effd13e
# ╟─07d3cb1b-01a8-441a-b731-83519c9ae94e
# ╟─dfdfb0a0-a157-4053-90b8-016b54101419
# ╟─9a7d108d-b8c3-483d-ae59-46c659dc000a
# ╠═016e53cc-919e-4aa1-88b3-95b560869b3b
# ╠═0dee1763-9ead-4693-b45d-e6e9367825a4
# ╠═8eeec730-65fb-4c56-b506-ed566e38a0ae
# ╠═d06ffc45-2fa3-4d15-a63d-5d4ed8c1536b
# ╟─63493e61-48fb-479f-973c-8dcf0ebf5097
# ╟─66ae2ff3-afd0-4753-99d6-56c4ca437482
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