FFT calculation of magnetic fields in air coils

The magnetostatic field produced by an air coil that possesses one-dimensional periodicity can be expressed as a one-dimensional discrete convolution of two functions. The first function expresses the field produced by a single turn of the coil. The second is a shape function; it expresses the spatial position and strength of current of each turn of the coil. The discrete convolution of these two functions gives the magnetostatic field produced by the coil. This paper presents one application of linear system theory to an air coil calculation, the use of the fast Fourier transform (FFT) in computing magnetostatic magnetic fields from air coils. A program is described which uses FFT convolution to perform this calculation.