94 lines
2.0 KiB
Julia
94 lines
2.0 KiB
Julia
include("showpicture.jl")
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using FFTW
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using Images
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using ImageView
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using Plots
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using .Showpicture
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function dft(f)
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if ndims(f) == 1
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M = length(f)
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[sum([x * exp(-2im*pi*u * (idx - 1) / M ) for (idx, x) in enumerate(f)]) for u=0:M-1]
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elseif ndims(f) == 2
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M, N = size(f)
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[sum([f[x+1, y+1] * exp(-2im*pi*(u*x/M + v*y/M)) for x=0:M-1, y=0:N-1]) for u=0:M-1, v=0:N-1]
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else
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error("Wrong dimension")
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end
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# mesh = [i * j for i=0:N-1, j=0:N-1]
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# W = exp.(-2im * pi * mesh / N)
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# W * f
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end
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function fft1d(array)
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#= https://en.wikipedia.org/wiki/Cooley%E2%80%93Tukey_FFT_algorithm
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#
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# Xk = Ek + e^(-2pi*i/N * k) * Ok
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#
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# Ek = Event DFT
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# Ok = Odd DFT
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#
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=#
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N = size(array)[1]
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if N == 1
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return array
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elseif N % 2 != 0
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error("Wrong dimension")
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end
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# people count from zero while julia counts from 1
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# either way, it should be the same name
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even = fft1d(array[1:2:end])
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odd = fft1d(array[2:2:end])
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w = exp.(-2im * pi / N * [i for i=0:N/2-1])
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half1 = even .+ (odd .* w)
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half2 = even .- (odd .* w)
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vcat(half1,half2)
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end
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function fft2d(matrix)
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if ndims(matrix) != 2
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error("I dont handle other than 2 dimension matrix")
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end
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matrix_fft1 = hcat(fft1d.(eachrow(matrix))...)
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hcat(fft1d.(eachrow(matrix_fft1))...)
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end
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if abspath(PROGRAM_FILE) == @__FILE__
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if (length(ARGS) < 1)
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println("fft library")
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display(fft(1:8))
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println()
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println("fft own implemenation")
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display(fft1d(1:8))
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println()
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println("DFT1D")
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display(dft(1:8))
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println()
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println("====================")
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println("fft2d library")
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display(fft([[1:8...] [1:8...]]'))
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println()
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println("fft2d own implemenation")
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display(fft2d([[1:8...] [1:8...]]'))
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println()
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println("DFT2D")
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display(dft([[1:8...] [1:8...]]'))
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println()
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else
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img = load(ARGS[1])
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img_gray = Float32.(Gray.(img))
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# img_fft = fft2d(Gray.(img))
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img_fft = fftshift(fft(img_gray))
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normalize = log.(abs.(img_fft)) .+ 1
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showpicture(normalize)
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end
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end
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