Fourier Function

Calculates the fourier spectrum of the data in argument 1. The function uses the 'Continuous Fourier' technique which numerically integrates the Fourier integral. Because this technique does not require the input data to be sampled at evenly spaced points, it doesn't suffer from frequency aliasing. This is the main drawback of the more commonly used FFT (Fast Fourier Transform) algorithm. However, the Continuous Fourier algorithm is much slower then the FFT, sometimes dramatically so.


Number Type Compulsory Default Description
1 real array Yes data
2 real Yes Fundamental frequency
3 real Yes Number of frequency terms
4 real array No options

Argument 1

The input data. This is expected to possess a reference i.e. x-values

Argument 2

Specifies the fundamental frequency. All terms calculated will be an integral multiple of this.

Argument 3

Specifies the number of frequency terms to be calculated.

Argument 4

This is optional and can be a 1 or 2 element array. The first element is the first frequency to be calculated expressed as a multiple of the fundamental. The default value is 0 i.e. the DC term is calculated first. The second element is the integration order used and may be 1 or 2.


Return type: complex array

The result of the calculation and will be a complex array with length equal to argument 3.