CartesianIndex(i::AbstractFFTIndex, inds::Tuple)
CartesianIndex(i::AbstractFFTIndex, A)

Constructs a CartesianIndex corresponding to the the index i using information from A or a set of axes ax.

AbstractFFTIndex{D}

Supertype for array indices that correspond to the frequency bins constructed by performing a Fourier transform of an array. This includes FFTIndex{D} and NormalizedFFTIndex{D}.

Usage

AbstractFFTIndex{D} serves as an index for any object indexable by CartesianIndex{D}. Although there is no direct method of converting an AbstractFFTIndex{D} to a CartesianIndex{D}, as that requires information about the array being indexed, instances of this type can be used as an

Indexing an array with an AbstractFFTIndex{D} is guaranteed to be an inbounds access.

Interface

For types T<:AbstractFFTIndex{D}:

• The length of an AbstractFFTIndex{D} is always D.
• The type constructors should accept a Tuple{Vararg{Integer}}. You will likely want to define

constructors that infer type parameters from the input. This will automatically define T(x::Vararg{Integer,D}).

• Tuple(::T) should be defined, returning the index as a NTuple{D,Int}.
• convert(::Type{<:FFTIndex}, ::T) should be defined. This is to allow for types that encode

information about normalization factors to be converted to an FFTIndex used by generic indexing methods. This will also automatically define (::Type{<:FFTIndex})(::T).

Like CartesianIndex{D} in Julia 1.10 and up, AbstractFFTIndex{D} is a scalar type. To iterate through its components, convert it to a Tuple with the Tuple constructor.

FFTAxis <: AbstractVector{Int}

The one-dimensional counterpart to FFTIndices, supporting only a single dimension. Its elements are plain Int types rather than the CartesianIndex of FFTIndices.

This type serves as an analog to Base.OneTo which is usually returned by axes; this package provides fftaxes to serve the same purpose.

Examples

julia> FFTAxis(4)
4-element FFTAxis:
 0
 1
 -2
 -1

FFTIndex{D} <: AbstractFFTIndex{D}

A index for an array corresponding to an FFT frequency bin along each dimension of an array. These frequency bins are integer values which are easily converted to corresponding array indices.

FFTIndices{D} <: AbstractArray{FFTIndex{D},D}

An iterable object defining a range of CartesianIndices corresponding to FFT indices. This can be used to convert a Cartesian array index to an FFT bin index, or vice versa.

An array of FFTIndex{D} objects which correspond to all valid indices of an indexable object.

The outputs use the convention where frequencies at or above the Nyquist frequency for that dimension are negative, matching the output of FFTW.fftfreq.

Examples

julia> FFTIndices(4)
4-element FFTIndices{1}:
 FFTIndex(0,)
 FFTIndex(1,)
 FFTIndex(-2,)
 FFTIndex(-1,)

julia> FFTIndices(3, 3)
3×3 FFTIndices{2}:
 FFTIndex(0, 0)   FFTIndex(0, 1)   FFTIndex(0, -1)
 FFTIndex(1, 0)   FFTIndex(1, 1)   FFTIndex(1, -1)
 FFTIndex(-1, 0)  FFTIndex(-1, 1)  FFTIndex(-1, -1)

FFTIndex._cartesian_tuple(i::AbstractFFTIndex, ax::Tuple)

Generates a Tuple which may be used to construct a CartesianIndex that performs the same indexing as i. This function is provided separately in case the CartesianIndex does not need to be constructed and a raw Tuple is desired.

fftaxes(a, d) -> FFTAxis

Returns an FFTAxis associated with an object a along dimension d. This is calculated from size(a, d).

fftaxes(a) -> NTuple{D,FFTAxis}

Returns a set of FFTAxis objects associated with an object a. This is calculated from size(a).