1970/12/01 by V. Cizek · 213 citations
Computer Science · Engineering · Mathematics · #Computer science #Digital Filter Design and Implementation #Discrete Fourier transform (general) #Discrete Hartley transform #Discrete sine transform #Fourier analysis #Fourier transform #Fractional Fourier transform #Geophysics and Sensor Technology #Hilbert spectral analysis #Hilbert transform #Hilbert–Huang transform #Image and Signal Denoising Methods #Mathematical analysis #Mathematics #Spectral density #Telecommunications #White noise
paper · doi:10.1109/tau.1970.1162139
published in IEEE Transactions on Audio and Electroacoustics 18(4), 340-343 (Institute of Electrical and Electronics Engineers)
crossref issued 1970/12/01 · crossref published 1970/12/01 · crossref published-print 1970/12/01 · openalex publication_date 1970/12/01 · crossref created 2004/04/30 · crossref deposited 2021/11/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/15 · crossref indexed 2026/07/30
The Hilbert transform H\f(t)\ of a given waveform f(t) is defined with the convolution H\f(t) = f(t) ∗ (1/\pit) . It is well known that the second type of Hilbert transform K0\f(x)\=φ(x) ∗ (1/2π)\cot(1)/(2)x exists for the transformed function f(tg(1)/(2)x)= φ(x) . If the function f(t) is periodic, it can be proved that one period of the H transform of f(t) is given by the H 1 transform of one period of f(t) without regard to the scale of tbe variable. On the base of the discrete Fourier transform (DFT), the discrete Hilbert transform (DHT) is introduced and the defining expression for it is given. It is proved that this expression of DHT is identical to the relation obtained by the use of the trapezoidal rule to the cotangent form of the Hilbert transform.