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Clarify normalization
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src/definitions.jl

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@@ -588,8 +588,9 @@ abstract type AdjointStyle end
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"""
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FFTAdjointStyle()
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Projection style for complex to complex discrete Fourier transforms.
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Projection style for complex to complex discrete Fourier transforms that normalize
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the output analogously to [`fft`](@ref).
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Since the Fourier transform is unitary up to a scaling, the adjoint simply applies
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the transform's inverse with an appropriate scaling.
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"""
@@ -598,8 +599,8 @@ struct FFTAdjointStyle <: AdjointStyle end
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"""
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RFFTAdjointStyle()
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Projection style for real to complex discrete Fourier transforms, for plans that
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halve one of the output's dimensions analogously to [`rfft`](@ref).
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Projection style for real to complex discrete Fourier transforms that halve
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one of the output's dimensions and normalize the output analogously to [`rfft`](@ref).
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Since the Fourier transform is unitary up to a scaling, the adjoint applies the transform's
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inverse, but with additional logic to handle the fact that the output is projected
@@ -610,9 +611,9 @@ struct RFFTAdjointStyle <: AdjointStyle end
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"""
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IRFFTAdjointStyle(d::Dim)
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Projection style for complex to real discrete Fourier transforms, for plans that
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expect an input with a halved dimension analogously to [`irfft`](@ref), where `d`
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is the original length of the dimension.
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Projection style for complex to real discrete Fourier transforms that expect
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an input with a halved dimension and normalize the output analogously to [`irfft`](@ref),
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where `d` is the original length of the dimension.
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Since the Fourier transform is unitary up to a scaling, the adjoint applies the transform's
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inverse, but with additional logic to handle the fact that the input is projected

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