A discrete Hartley transform based on Simpson's rule.

Abstract

The Discrete Hartley Transform and Discrete Fourier Transform are classical transfor- mations designed for e cient computations in the frequency domain. We introduce a relatively new transformation based on the existing Discrete Hartley Transform by applying Simpson's quadrature for N = 4m + 2 quadrature nodes. The majority of our investigation involves exploring the mathematical properties satis ed by our newly derived transformation. We formulate the convolution and cross correlation properties both in the real and frequency domain. An intensive spectral analysis is performed to ascertain the multiplicities of the eigenvalues corresponding to the transformation matrix.