Add fft op

Author: nHackel

docs/src/tutorials/fft.jl

@@ -0,0 +1,18 @@
+# # Fourier Operator
+include("../../util.jl") #hide
+# The Fourier operator and its related operators for the discrete cosine and sine transform are available
+# whenever FFTW.jl is loaded together with LinearOperatorCollection:
+fop = FFTOp(Complex{eltype(image)}, shape = (N, N))
+cop = DCTOp(eltype(image), shape = (N, N))
+sop = DSTOp(eltype(image), shape = (N, N))
+image_frequencies = reshape(fop * vec(image), N, N)
+image_cosine = reshape(cop * vec(image), N, N)
+image_sine = reshape(sop * vec(image), N, N)
+
+fig = Figure()
+plot_image(fig[1,1], image, title = "Image")
+plot_image(fig[1,2], abs.(weighted_frequencies) .+ eps(), title = "Frequency Domain", colorscale = log10)
+plot_image(fig[1,3], image_cosine, title = "Cosine")
+plot_image(fig[1,4], image_sine, title = "Sine")
+resize_to_layout!(fig)
+fig