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fourier.jl
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fourier.jl
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### A Pluto.jl notebook ###
# v0.19.17
using Markdown
using InteractiveUtils
# ╔═╡ 6d0df444-a486-11ed-2dc7-93a0b5587a72
using FFTW
# ╔═╡ 69c8e55d-6600-47fd-a357-97fbb3fcd614
using CairoMakie
# ╔═╡ 747fc355-8143-46c1-a2e2-a0983f371d8b
f(x) = sin(4x)
# ╔═╡ 6e8d88e4-0fd6-4c9f-991c-6dcdddac15b7
L = 5.0
# ╔═╡ c85033eb-3a40-4d6c-9d74-2aac300ec96a
N = 100
# ╔═╡ dfd5e555-877b-428b-84d6-799e42b18eb9
xs = range(-L, L; length=N)
# ╔═╡ 41089329-f72d-4617-a03e-515b1bca7dfb
ys = map(f, xs)
# ╔═╡ fa2502f2-3f06-48cb-b521-5b790e98a15a
ks = 0.0:N-1.0
# ╔═╡ 3b30f8a9-673a-446f-9d7b-0cd9532c586b
As = fft(ys)
# ╔═╡ 75262072-d754-4a24-a42f-b48b806af44d
iys = ifft(As)
# ╔═╡ aaae1fd8-31f9-48e9-a4e6-c23262528d00
let fig = Figure()
ax = Axis(fig[1, 1])
lines!(ax, xs, real.(ys))
lines!(ax, xs, imag.(ys))
lines!(ax, xs, real.(iys))
lines!(ax, xs, imag.(iys))
fig
end
# ╔═╡ 2306885b-593a-4257-b953-255641174811
let fig = Figure()
ax = Axis(fig[1, 1])
lines!(ax, ks, real.(As))
lines!(ax, ks, imag.(As))
fig
end
# ╔═╡ 00000000-0000-0000-0000-000000000001
PLUTO_PROJECT_TOML_CONTENTS = """
[deps]
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[compat]
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"""
# ╔═╡ 00000000-0000-0000-0000-000000000002
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