Abstract
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.
Highlights
Hilbert transform (HT) plays an essential role in constructing analytic signals for a variety of signal and image processing applications
In this work we introduce a method for computation of HT based on the discrete cosine transform (DCT)
In this work we introduce a new method for computation of HT, which is based on the discrete cosine transform (DCT) [17,18,19,20,21]
Summary
Hilbert transform (HT) plays an essential role in constructing analytic signals for a variety of signal and image processing applications. In this work we introduce a new method for computation of HT, which is based on the discrete cosine transform (DCT) [17,18,19,20,21]. The DCT has become the industry standard in signal processing society (digital filtering, data compression, image coding, HDTV etc.). The properties of the DCT are very close to the statistically optimal Karhunen-Loeve transform (KLT) for a large number of signal families. We review the FFT-based method for computation of the analytic signal. We introduce the DCT based method for computation of HT and describe some experimental results
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