Discrete Fourier transform: Difference between revisions

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=={{header|Julia}}==
The cispi function was added in Julia 1.6. The cispi of x is e to the power of (pi times i times x). Other syntax, such as {T,N} in the function signature and real() and tuplentuple() in the loop, is designed to support arbitrary dimensional arrays and to cue the compiler so as to have mostly constants in the loop at runtime, speeding run time with large arrays.
<lang julia>function dft(A::AbstractArray{T,N}) where {T,N}
F = zeros(complex(float(T)), size(A)...)
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end
 
const seq = [2, 3, 5, 7, 11]
const fseq = dft(seq)▼
newseq = idft(fseq)
println("$seq =>\n$fseq =>\n$newseq =>\n", Int.(round.(newseq)))▼
 
seq2 = [2 7; 3 11; 5 13]
▲const fseq = dft(seq)
fseq = dft(seq2)
 
const newseq = idft(fseq)
println("$seq2 =>\n$fseq =>\n$newseq =>\n", Int.(round.(newseq)))
 
▲println("$seq =>\n$fseq =>\n$newseq =>\n", Int.(round.(newseq)))
</lang>{{out}}
<pre>
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ComplexF64[2.0000000000000013 - 1.4210854715202005e-15im, 2.999999999999996 + 7.993605777301127e-16im, 5.000000000000002 + 2.1316282072803005e-15im, 6.999999999999998 - 8.881784197001252e-16im, 11.0 + 0.0im] =>
[2, 3, 5, 7, 11]
[2 7; 3 11; 5 13] =>
ComplexF64[41.0 + 0.0im -21.0 + 0.0im; -7.000000000000002 + 3.46410161513775im 3.0000000000000053 + 7.105427357601002e-15im; -6.9999999999999964 - 3.4641016151377606im 3.0000000000000053 + 7.105427357601002e-15im] =>
ComplexF64[2.000000000000002 + 5.921189464667501e-16im 6.999999999999997 - 4.144832625267251e-15im; 2.9999999999999996 - 8.881784197001252e-16im 11.000000000000002 + 1.0362081563168128e-15im; 4.999999999999999 + 0.0im 13.000000000000002 + 1.924386576016938e-15im] =>
[2 7; 3 11; 5 13]
</pre>
 
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