Hilbert transform is a basic tool in constructing analytical signals for a various applications such as amplitude modulation, envelope and instantaneous frequency analysis, quadrature decoding, shift-invariant multi-r...Hilbert transform is a basic tool in constructing analytical signals for a various applications such as amplitude modulation, envelope and instantaneous frequency analysis, quadrature decoding, shift-invariant multi-rate signal processing and Hilbert-Huang decomposition. This work introduces a complex Hilbert transform (CHT) filter, where the real and imaginary parts are a Hilbert transform pair. The CHT filtered signal is analytic, i.e. its Fourier transform is zero in negative frequency range. The CHT filter is constructed by half-sample delay operators based on the B-spline transform interpolation and decimation procedure. The CHT filter has an ideal phase response and the magnitude response is maximally flat in the frequency range 0 ≤ ω ≤ π. The CHT filter has integer coefficients and the implementation in VLSI requires only summations and register shifts. We demonstrate the feasibility of the CHT filter in reconstruction of the sign modulated CMOS logic pulses in a fibre optic link.展开更多
Noise is the biggest obstacle that makes the incipient fault diagnosis results of roller bearings uncorrected; a new method for diagnosing incipient fault of roller bearings based on the Wavelet Transform Correlation ...Noise is the biggest obstacle that makes the incipient fault diagnosis results of roller bearings uncorrected; a new method for diagnosing incipient fault of roller bearings based on the Wavelet Transform Correlation Filter and Hilbert Transform was proposed. First, the weak fault information features are picked up from the roller bearings fault vibration signals by use of a de-noising characteristic of the Wavelet Transform Correlation Filter as the preprocessing of the Hilbert Envelope Analysis. Then, in order to get fault features frequency, de-noised wavelet coefficients of high scales which represent high frequency signal were analyzed by Hilbert Envelope Spectrum Analysis. The simulation signals and diagnosing examples analysis results reveal that the proposed method is more effective than the method of direct wavelet coefficients-Hilbert Transform in de-noising and clarifying roller bearing incipient fault.展开更多
An application of the sinc sum function in Hilbert transformer (HT) is studied. The expression of the frequency re- sponse of HT is expressed with sinc sum functions. Some properties of sub-amplitude response of HT ar...An application of the sinc sum function in Hilbert transformer (HT) is studied. The expression of the frequency re- sponse of HT is expressed with sinc sum functions. Some properties of sub-amplitude response of HT are proved by using the properties of the sinc sum function. A general HT formula is obtained theoretically and it contains a general window function. As an example three new window functions are obtained. Different from the existing window func- tions obtained from lowpass filters, these window functions are obtained directly from HT. Comparisons show that new windows are better than the Hanning, Hamming, Blackman and Kaiser windows in terms of HT performances.展开更多
文摘Hilbert transform is a basic tool in constructing analytical signals for a various applications such as amplitude modulation, envelope and instantaneous frequency analysis, quadrature decoding, shift-invariant multi-rate signal processing and Hilbert-Huang decomposition. This work introduces a complex Hilbert transform (CHT) filter, where the real and imaginary parts are a Hilbert transform pair. The CHT filtered signal is analytic, i.e. its Fourier transform is zero in negative frequency range. The CHT filter is constructed by half-sample delay operators based on the B-spline transform interpolation and decimation procedure. The CHT filter has an ideal phase response and the magnitude response is maximally flat in the frequency range 0 ≤ ω ≤ π. The CHT filter has integer coefficients and the implementation in VLSI requires only summations and register shifts. We demonstrate the feasibility of the CHT filter in reconstruction of the sign modulated CMOS logic pulses in a fibre optic link.
文摘Noise is the biggest obstacle that makes the incipient fault diagnosis results of roller bearings uncorrected; a new method for diagnosing incipient fault of roller bearings based on the Wavelet Transform Correlation Filter and Hilbert Transform was proposed. First, the weak fault information features are picked up from the roller bearings fault vibration signals by use of a de-noising characteristic of the Wavelet Transform Correlation Filter as the preprocessing of the Hilbert Envelope Analysis. Then, in order to get fault features frequency, de-noised wavelet coefficients of high scales which represent high frequency signal were analyzed by Hilbert Envelope Spectrum Analysis. The simulation signals and diagnosing examples analysis results reveal that the proposed method is more effective than the method of direct wavelet coefficients-Hilbert Transform in de-noising and clarifying roller bearing incipient fault.
文摘An application of the sinc sum function in Hilbert transformer (HT) is studied. The expression of the frequency re- sponse of HT is expressed with sinc sum functions. Some properties of sub-amplitude response of HT are proved by using the properties of the sinc sum function. A general HT formula is obtained theoretically and it contains a general window function. As an example three new window functions are obtained. Different from the existing window func- tions obtained from lowpass filters, these window functions are obtained directly from HT. Comparisons show that new windows are better than the Hanning, Hamming, Blackman and Kaiser windows in terms of HT performances.
