From 00eef4f5e54ba3275a5907a6a21fa336e694790d Mon Sep 17 00:00:00 2001 From: Gaurav Arya Date: Wed, 19 Jul 2023 15:05:14 -0400 Subject: [PATCH] Clarify normalization --- src/definitions.jl | 15 ++++++++------- 1 file changed, 8 insertions(+), 7 deletions(-) diff --git a/src/definitions.jl b/src/definitions.jl index e495104..4c59b00 100644 --- a/src/definitions.jl +++ b/src/definitions.jl @@ -588,8 +588,9 @@ abstract type AdjointStyle end """ FFTAdjointStyle() -Projection style for complex to complex discrete Fourier transforms. - +Projection style for complex to complex discrete Fourier transforms that normalize +the output analogously to [`fft`](@ref). + Since the Fourier transform is unitary up to a scaling, the adjoint simply applies the transform's inverse with an appropriate scaling. """ @@ -598,8 +599,8 @@ struct FFTAdjointStyle <: AdjointStyle end """ RFFTAdjointStyle() -Projection style for real to complex discrete Fourier transforms, for plans that -halve one of the output's dimensions analogously to [`rfft`](@ref). +Projection style for real to complex discrete Fourier transforms that halve +one of the output's dimensions and normalize the output analogously to [`rfft`](@ref). Since the Fourier transform is unitary up to a scaling, the adjoint applies the transform's inverse, but with additional logic to handle the fact that the output is projected @@ -610,9 +611,9 @@ struct RFFTAdjointStyle <: AdjointStyle end """ IRFFTAdjointStyle(d::Dim) -Projection style for complex to real discrete Fourier transforms, for plans that -expect an input with a halved dimension analogously to [`irfft`](@ref), where `d` -is the original length of the dimension. +Projection style for complex to real discrete Fourier transforms that expect +an input with a halved dimension and normalize the output analogously to [`irfft`](@ref), +where `d` is the original length of the dimension. Since the Fourier transform is unitary up to a scaling, the adjoint applies the transform's inverse, but with additional logic to handle the fact that the input is projected