This program performs Trigonometric Interpolation using the Discrete Fourier Transform (DFT) and the Inverse Discrete Fourier Transform (IDFT). It is designed to find a trigonometric polynomial that passes through a given set of data points.
Trigonometric interpolation is a type of interpolation where the interpolating function is a trigonometric polynomial. This is particularly useful when the data points are equally spaced, in which case the solution can be efficiently computed using the DFT and IDFT.
The DFT converts a sequence of equally spaced samples of a function into a sequence of coefficients of a finite combination of complex sinusoids, ordered by their frequencies. It is a fundamental tool in digital signal processing and data analysis.
The IDFT is the inverse operation of the DFT. It converts the sequence of coefficients obtained from the DFT back into the original sequence of data points.