Pseudo Spectral Method Based on Symmetric Extension

Abstract

Pseudo spectral (PS) method using discrete Fourier transform (DFT) is a calculation method of obtaining the derivative in the frequency domain. When the sequence is discontinuous at its both sides, oscillatory approximation is obtained by PS method using DFT (PS-DFT). To overcome this problem, we study the PS method based on symmetric extension, where discrete cosine transform (DCT) Type 1 and Type 2 are considered as the forward transform. Analyzing the PS-DFT of the symmetrically extended sequence, we derive the constants multiplied by the DCT coefficients and the inverse transform in the PS context. We compare two PS methods based on symmetric extension with PS-DFT. We evaluate the accuracy of the derivative obtained by two PS methods on symmetric extension using known derivative. Application to image interpolation is demonstrated.