```
#Ref : https://www.cs.cornell.edu/~bindel/class/cs5220-s10/slides/FFT.pdf
#page 17
#run(`$(Base.julia_cmd())`)
using LinearAlgebra
function getBitReversed(N)
m = Int64(log2(N))
return [parse(Int64,reverse(bitstring(i)[end-m+1:end]),base = 2) for i in 0:N-1]
end
function getMatrices(N)
#N = 4
t = Int64(log2(N))
As = []
for q = 1:t
L = 2^q
Lby2 = 2^(q-1)
r = Int64(N/L)
I_r = Matrix(1.0I,r,r)
tw = exp.(-2im*pi*(0:Lby2-1)/L)
D = diagm(tw)
B_r = [Matrix(1.0I,Lby2,Lby2) D;Matrix(1.0I,Lby2,Lby2) -D]
A_q = kron(I_r,B_r)
push!(As,A_q)
end
return As
end
function test()
N = 16
P = 1im*zeros(N,N)
ind = getBitReversed(N) .+ 1
for i in Base.OneTo(N)
P[i,ind[i]] = 1.0
end
As = getMatrices(N)
F_ct = copy(P)
for i in Base.OneTo(length(As))
#println("A",i)
#display(As[i])
F_ct = As[i]*F_ct
end
F_N = exp.(-2im*pi*(0:N-1)*(0:N-1)'/N)
#=
println("F_n")
display(F_N)
println("F_ct")
display(F_ct)
=#
println(isapprox(F_N,F_ct))
return F_N,As,P
end
F_N,As,P = test();
```

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## Top comments (3)

`exp.(-2im*pi*(0:Lby2-1)/L)`

could be`cispi.(-2*(0:Lby2-1)/L)`

which will be slightly faster and more accurate.It would have been better if you wrote some text explaining what this is all about. We CANNOT read your mind and we don't know what context or usefulness of the code.

I have mentioned the page #13 of the reference. Anyway I will try to add some comments.