A package implementing efficient, multi-dimensional Fourier interpolation that is more convenient than FFTs when using hierarchical grids and when the number of coefficients is small compared to the number of evaluation points.


As a first example, we evaluate cosine from its Fourier series coefficients:

julia> using FourierSeriesEvaluators

julia> cosine = FourierSeries([0.5, 0.0, 0.5], period=2pi, offset=-2)
3-element and (6.283185307179586,)-periodic FourierSeries with Float64 coefficients, (0,) derivative, (-2,) offset

julia> cosine(pi)
-1.0 + 0.0im

Notice that we can create a series object and interpolate with a function-like interface. For more examples, see the documentation.


Generic Fourier series can be implemented with the AbstractFourierSeries interface and the following implementations are provided as building blocks for others:

Additionally, memory management for parallel workloads is supported by FourierWorkspace.

Extended help

The package also provides the following low-level routines that are also useful

These routines have the following features

  • Support for abstract (esp. offset) coefficient arrays and array-valued coefficients
  • Support for evaluation in the complex plane
  • Evaluation of derivatives of the Fourier series with Fourier multipliers