# conv_via_fft.jl 2D FFT for filtering
using MIRT: jim
using Plots; default(titlefontsize=6, labelfontsize=6, legendfontsize=6,
	tickfontsize=5,) # adjust these as needed to for your plot

using LaTeXStrings
using FFTW: fft, ifft, fftshift, ifftshift

rect(x) = abs(x) < 1/2 # convenient function

nx = ?; ny = ? # sampling parameters
dx = ?; dy = ?
x = (-nx/2:nx/2-1) * dx # sample locations in x
y = ?
fxy = ? # (samples of) the image f(x,y)
pl = Array{Any}(nothing, 3,3)
pl[1] = jim(x, y, fxy, title=L"f(x,y)", xlabel=L"x", ylabel=L"y")

# find the 2D FFT of the image
# hint: fftshift() will be important somewhere near here!

F = ?
u = ? # frequency sample positions (ν_X)
v = ? # frequency sample positions (ν_Y)

# display spectrum F of f(x,y)
pl[4] = jim(u, v, abs.(F), title=L"|F(\nu_X,\nu_Y)|",
	xlabel=L"\nu_X", ylabel=L"\nu_Y")
pl[5] = jim(u, v, real.(F), title=L"F_R(\nu_X,\nu_Y)",
	xlabel=L"\nu_X", ylabel=L"\nu_Y")
pl[6] = jim(u, v, imag.(F)*1e17, title=L"F_I(\nu_X,\nu_Y) \cdot 10^{17}",
	xlabel=L"\nu_X", ylabel=L"\nu_Y")

# Create (samples of) filter frequency response, and display
H = ?

pl[3] = jim(u, v, H, title=L"H(\nu_X,\nu_Y)",
	xlabel=L"\nu_X", ylabel=L"\nu_Y")

# Find spectrum of output image using convolution property of 2D FT
G = ?

# Find final image by returning to image domain
# Watch out for fftshift() again!
g = ?

# display real and imaginary parts of g(x,y)
# Hint: does your imaginary part make sense?
pl[7] = jim(x, y, real.(g), title=L"g_R(x,y)",
	xlabel=L"x", ylabel=L"y")
pl[8] = jim(x, y, imag.(g), title=L"g_I(x,y)",
	clim = (-1,1), xlabel=L"x", ylabel=L"y")
pl[9] = jim(x, y, abs.(g), title=L"|g(x,y)|",
	xlabel=L"x", ylabel=L"y")

maximum(abs.(imag.(g))) / maximum(abs.(g)) # check imaginary part

pl[2] = plot(legend=false, grid=false, foreground_color_subplot=:white) # blank
plot(pl...)
#savefig("conv_via_fft.pdf")