A discrete Fourier transform based on Simpson%26apos;s rule

作者：Singh P^*; Singh V

来源：Mathematical Methods in the Applied Sciences, 2012, 35(2): 151-157.

DOI：10.1002/mma.1547

• discrete Fourier transform
• Simpson%26apos
• s rule
• circular convolution

Fourier analysis plays a vital role in the analysis of continuous-time signals. In many cases, we are forced to approximate the Fourier coefficients based on a sampling of the time signal. Hence, the need for a discrete transformation into the frequency domain giving rise to the classical discrete Fourier transform. In this paper, we present a transformation that arises naturally if one approximates the Fourier coefficients of a continuous-time signal numerically using the Simpson quadrature rule. This results in a decomposition of the discrete signal into two sequences of equal length. We show that the periodic discrete time signal can be reconstructed completely from its discrete spectrum using an inverse transform. We also present many properties satisfied by this transform.

• 出版日期2012-1-30