# How to use fft to 2d vector data

**URL:** <https://discourse.julialang.org/t/how-to-use-fft-to-2d-vector-data/98530>\
**Category:** Signal and Image Processing\
**Tags:** package\
**Created:** [May 9, 2023, 6:27am UTC](https://discourse.julialang.org/t/how-to-use-fft-to-2d-vector-data/98530 "2023-05-09T06:27:31Z")\
**Posts on this page:** 3\
**Page:** 1

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**Author:** ![xiaoming](https://avatars.discourse-cdn.com/v4/letter/x/a6a055/32.png) [@xiaoming](https://discourse.julialang.org/u/xiaoming)\
**Post date:** [May 9, 2023, 6:27am UTC](https://discourse.julialang.org/t/how-to-use-fft-to-2d-vector-data/98530/1 "2023-05-09T06:27:31Z")

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I have some data like this:

```julia
function f(x)
    [sin(2*pi*x[1])*cos(2*pi*x[2]), cos(2*pi*x[1])*sin(2*pi*x[2])]
end
N=200
data = [f([i/N,j/N]) for i in 0:N-1, j in 0:N-1]

```

which is a matrix of size N\times N, with vector elements. Now I want to take fft in each slice of `data` so that the result has the same structure as `data`. I can do this by using the follow codes

```julia
using FFTW
function v_fft(A::Matrix{Vector{Float64}})
    n=size(A,2)
    b=Matrix{Float64}(undef, n, n)
    c=Matrix{Float64}(undef, n, n)
    @inbounds @simd for i in 1:n^2
        b[i]=A[i][1]
        c[i]=A[i][2]        
    end
    fb=fft(b)
    fc=fft(c)
    result=Matrix{Vector{ComplexF64}}(undef, n, n)
    @inbounds @simd for i in 1:n^2
        result[i]=[fb[i],fc[i]]       
    end
    result
end

```

`v_fft(data)` gives what I want. Is there any simple way to do that ?

---

<div class="post-metadata">

**Author:** ![bertschi](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/bertschi/32/33462_2.png) [@bertschi](https://discourse.julialang.org/u/bertschi)\
**Post date:** [May 9, 2023, 5:06pm UTC](https://discourse.julialang.org/t/how-to-use-fft-to-2d-vector-data/98530/2 "2023-05-09T17:06:02Z")

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In the nested format there is probably no easier way. Using instead an `N x N x 2` matrix layout, you could use `eachslice`, broadcasting and `stack`:

```julia
julia> using Compat

julia> datamat = permutedims(stack(data), (2, 3, 1));

julia> size(datamat)
(200, 200, 2)

julia> res = stack(fft.(eachslice(datamat; dims = 3)));

julia> res[:, :, 1] == first.(v_fft(data))
true

julia> size(res)
(200, 200, 2)

```

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<div class="post-metadata">

**Author:** ![xiaoming](https://avatars.discourse-cdn.com/v4/letter/x/a6a055/32.png) [@xiaoming](https://discourse.julialang.org/u/xiaoming)\
**Post date:** [May 10, 2023, 1:17am UTC](https://discourse.julialang.org/t/how-to-use-fft-to-2d-vector-data/98530/3 "2023-05-10T01:17:02Z")

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Thank you! This works for me.