Computation of Hilbert Transform via Discrete Cosine Transform

• 作者: Hannu Olkkonen Juuso T. Olkkonen Peitsa Pesola
• 来源期刊: 信号与信息处理(英文)
• 学科: 数学
• 关键词: HILBERT TRANSFORM ANALYTIC Signal ENVELOPE Analysis FFT
• 年，卷（期）: 2010,（1）
• 页码范围: 18-23
• 页数: 6页
• 分类号: O1

摘要

Hilbert transform (HT) is an important tool in constructing analytic signals for various purposes, such as envelope and instantaneous frequency analysis, amplitude modulation, shift invariant wavelet analysis and Hilbert-Huang decomposition. In this work we introduce a method for computation of HT based on the discrete cosine transform (DCT). We show that the Hilbert transformed signal can be obtained by replacing the cosine kernel in inverse DCT by the sine kernel. We describe a FFT-based method for the computation of HT and the analytic signal. We show the usefulness of the proposed method in mechanical vibration and ultrasonic echo and transmission measurements.