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The IIR allpass fractional-delay fractional Hilbert transformer is designed in the complex-cepstrum domain. The maximal flatness criterion on the phase response is considered for the midband frequency. Two independent systems of linear equations are formulated, resulting in closed-form solutions of the even-index and odd-index parts of complex cepstrum of the denominator polynomial. Moreover, they...
This paper presents the closed-form designs of an infinite-impulse-response (IIR) Hilbert transformer with an integer delay. The maximally flat criterion is applied at the midband frequency π/2. These designs are further categorized into eight types according to the filter orders and the delay values being even or odd. Their coefficients can be explicitly solved in closed form. A recursive relation...
In this paper, we define the short-response Hilbert transform (SRHLT) and use it for edge detection. The SRHLT has a parameter b. When b = 0, it becomes the Hilbert transform (HLT). When b is infinite, it becomes differentiation. Many edge detection algorithms are based on differentiation. However, they are sensitive to noise. By contrast, when using the HLT for edge detection, the noise is reduced...
We propose a design of discrete Fractional Hilbert transformer. Through the time domain analysis of the ideal input and output signal of a LTI system, we derived equations which can be solved numerically for the filter's impulse response. The conventional Hilbert transformer is derived as a special case of the fractional Hilbert transformer. We also show that the difference between the designed system...
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